What you're asking touches on dialect, register, and genre. Any ancient language that is attested has a finite corpus of literature. Within a given corpus, we can divide texts up into genres. Legal codes would be a particular genre. In medieval literature, saints' lives was a very popular genre. You'll also find epic poetry, exegesis, and historical texts. These genres usually have conventions and formulas, but sometimes break from them as well. The language is often in a standardized literary register, but not always.

Let's look at some old languages. I'm not familiar with Egyptian, but I can tell you about a language that's just a little bit older-

Sumerian.

We have records of Sumerian that span a good 3000 years, and to a certain extent it's standardized. There were handful of scribal schools and we can identify tendencies from each of those schools, but it's hard to say what constitutes a dialect in Sumerian. The most well-understood "dialect" is called eme.sal, and is often thought to be a register of the language used by women, but that has been called into question. The truth is, we don't know exactly why eme.sal was used, and we don't know exactly what features where characteristic of particular times, places, or schools. We do know that these scribal schools were teaching scribes to read and write Sumerian well after the language ceased to be spoken. Interestingly, scribes who spoke Sumerian natively tended to leave out quite a bit of grammatical information, while later scribes whose first language was Akkadian would include more case endings and verbal infixes for clarity.

Many modern students of Sumerian will begin by studying formulaic temple dedications that were stamped into bricks. These go something like "En-Lil nin-ani Ur-Nammu lugal kiengi kiuri-ke e mu-na-du", that is "Ur-Nammu, king of Sumer and Akkad, for his lord En-lil, built the temple." Just remove the name of the god and the name of the king and you basically have the same inscriptions stamped on bricks all over temples. It's such a repetitve formula that it becomes easy to read very quickly.

But there's more to the Sumerian corpus than dedication bricks. We also have poetry, letters, law codes, grammar tablets, records of business transactions, and tax records. Some of it is incredibly boring and formulaic, while some of it is incredibly fascinating. You can read some letters between kings and government officials here: http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=c.3.1*#

To what extent can we say that any of this is representative of how people actually spoke? Well, we can't really. But we can look for simple, clear sentences that seem as appropriate in a casual conversation as they would in a flowery praise poem. Here is line 70 from the first Sumerian Gilgamesh poem:

"lu2 še lugal-ĝu10 in-nu"

"That man is not my king."

While most of the poem uses pretty grandiose language, this sentence is so stylistically straightforward that it could as easily have been spoken by a random dude from Ur. You can scan the translations of the corpus for more sentences like this and then look for the corresponding line in Sumerian.

Akkadian

I'm not very familiar with Akkadian, but there is one text you might find particularly interesting, and hilarious: https://en.wikipedia.org/wiki/Complaint_tablet_to_Ea-nasir

Old English

Most of the Old English is in the West Saxon dialect. This was used as a literary standard due the political significance of Winchester at the time. We do have texts in other dialects, though not as many. It's impossible to say how well any of these texts represent everyday speech. Old English literature is quite varied and extends well beyond legal texts: https://en.wikipedia.org/wiki/Old_English_literature

Like the simple Sumerian sentence above, we can also look for moments where the texts drop a certain level of formula and formality. One of my favorite moments in OE literature is from the translation of Apollonius of Tyre, where the titular character, having gotten himself into some trouble, talks to himself in the 3rd person:

"He cwaeþ þa to him silfum. 'Hwaet dest þu nu, Apolloni?'"

"He said then to himself, 'What are you going to do now, Apollonius?'"

While this is a translation of a Latin text, it's hard not to imagine the Anglo-Saxon translator forgoing the literary style of the narration in order to paint the picture of a forlorn Apollonius shaking his head and muttering to himself.

We also see a nice, to-the-point line capping off the opening of Beowulf. After extolling the virtues of Scyld Scefing in lofty alliterative verse, the poet tells us: "Þæt wæs god cyning!" That was a good king. This kind of simple, everyday sentence is completely unlike the lines that precede it. This is just the kind of thing that someone could say without necessarily having to be from a poem. In a way, breaking with poetic convention is something of a convention. It serves as a device, a sort of thesis statement, to drive the point home.

One of the most well-know Old English writers was a monk named Aelfric. Aelfric has a very straightforward manner of writing. One of the texts modern students of Old English will often start with is his Colloquy on Occupations. A teacher and his students discuss the merits of various jobs. While it's a translation from Latin into OE, it does give a sense of conversational Old English: https://en.wikisource.org/wiki/%C3%86lfric%27s_Colloquy

Middle Welsh

Some of the speech in Middle Welsh literature serves as a counterpoint to what we see in the Colloquy. The most famous work of Middle Welsh literature is the Mabinogion. The Mabingion is somewhere between mythology and fairy tales. It's kind of its own genre, really. The narrative is rather stiff and formulaic, but what I love about it is that it has lots of dialogue. My favorite moment of dialogue goes like this- Pwyll has been chasing Riannon on horseback but can't catch up (because magic), and his horse is exhausted:

Yna y dywot Pwyll. "A uorwyn," heb ef, " yr mwyn y gwr mwyhaf a gery, arho ui!"

Then Pwyll said, "Maiden, for the sake of the man you love most, await me!"

"Arhoaf yn llawen," heb hi, "ac oed llessach y'r march, pei ass archut yr meityn."

"I will wait, glady," she said, "but it would have been better for the horse if you had asked sooner."

Sewyll, ac arhos a oruc y uorwyn, a gwaret y rann a dylyei uot am y hwyneb o wisc y phenn, ac attal y golwc arnaw, a dechreu ymdidan ac ef.

The maiden stood and waited, and removed the piece of garment (veil) from her face, and glanced upon him, and began to converse with him.

"Arglwydes," heb ef, "pan doy di, a pha gerdet yssyd arnat ti?"

"Lady," he said, "whence do you come, and what errand is upon you?"

Part of the medievalieness of the translation just comes from trying to stay close to the wording of the original, but this passage gives us a little of the flavor of language we might hear when a nobleman and noblewoman converse. What I find particularly interesting is that Riannon gets a little snarky with her comment about the horse (and she also takes off her veil!). This makes the interaction feel more natural than some of the other dialogue from these stories, yet the author maintains the literary register even in the direct speech. Was this how nobles spoke to each other in 12th century Wales? Maybe not exactly like this, but it certainly gives us a better idea than a legal text.

I can’t answer this too in depth but just a quick note on the Egyptian language is that we do actually have a bunch of writings that are not monuments or scribal records, but also personal letters and general notes people wrote onto scraps of pottery, shopping list kinda stuff. Obviously this is still a bit skewed, as you’d have to be literate to read/write that, which limits the number and class of person quite a lot and we can’t really tell how the words were actually said a lot of the time and if there were artifactual spellings like in knight, but still gives us a bit of an idea on the language use. Egyptian is also a bit easier to tell the difference because it had several scripts by the Middle Kingdom, the general use demotic script, the more formal priestly one used on papyrus called hieratic, and the super formal old kingdom hieroglyphics put on tombs and monuments. The ‘alphabets’ for these were all the same, at least from what I studied, but the actual ‘letter’ used differs, and some grammar rules did as well, at least with hieroglyphs.

When you have a long record like we do with Egyptian, or writings on grammar like we do with Greek and Latin, you can spot differences, because eventually, the common use tends to become the one used even by the more formal writings (for example, our legal documents are written in English from like the 1800s, not the 1200s). Misspellings are always great for this, where someone trying to use the formal conventions messes up and puts in either a similar sounding letter or the letter likely used in common speech (such as writing nife and not knife). If anything, this is probably the take away, yes, it is skewed, but we know it is skewed and we know the things to look for to counter that skew as much as we can.

In regards to your example of modern legal documents, the reason that language is so different is actually a different linguistic phenomenon of loan words, that is words that are taken from different languages to use for certain concepts or to add a certain class to their use age. Like in most English technical jargons today, legal speech is filled with Latin and Greek loan words because at the time period most of this stuff was codified, the educated classes using it all knew these classical languages and so decided to use them for 1, consistency since all Europe knew them whether or not they spoke English, 2, being not commonly used terms they could be attributed a very specific meaning without being confused to to the word being used in other contexts, and 3, it gave it distinction, formality and power that separates its users from the commoners. An example from biology, the formal name for white blood cells is leukocytes. This is literally white cell in Greek, but since few English speakers use Greek, it’s able to be a specific medical term that won’t come up in other contexts and confuse people, whereas calling them white cells could be confusing to patients and lesser trained doctors who might get it confused with other cells, or even more general things is the more literal translation of ‘white container’ is used (think of the cell part as the same meaning as jail cell, that of a hollow space). Loan words are pretty easy to spot linguistically though, they are made of uncommon sound combinations, have unusual beginnings or endings, and often follow different grammar rules (for example, English words ending in -os/-us are usually Greek loan words).

The other thing to note is that outside of the situation of loan words (which are something English is full of, we have two words for nearly everything, one Germanic and one Romance based), differences in language between contexts and classes is far more often simply pronunciation or grammar differences, using completely different words or sounds is unusual.

TLDR: Yes, it’s biased a bit, but linguists know this and know what to look for to balance this, and we do often have examples of less formal writings. Also, the differences are less than you’d think outside of languages with significant loan words (like English), often just being pronunciation or grammar.

Oh! Same vein, so this counts as a follow up:

In regards to these various forms of language and how little we know, I've heard that what Ancient Roman citizens actually spoke was significantly different dialect of Latin than we see in documents and inscriptions.

How true is this? Would the common Roman understand or be able to write in the 'fancier' Latin? Would a Roman official, say a Senator, or Consul or the Emperor be well versed in 'common' Latin?