Historical linguist here. I've got a few insights, but you may be interested in asking on r/linguistics to find some more experts on the subject.

I can't speak to whether "life was just experienced in a more formal way back then". We may have that impression about the past (in certain cultures) but it may have more to do with the type of language used in surviving records. Today, we can find recorded examples of casual language pretty easily (e.g. on Reddit, Youtube) because it's easy to self-publish and we have a culture of publishing informal things. But depending on what era you're talking about, having your voice recorded and/or writing something down in a form likely to last was a bigger deal, so the language we see in those records is not necessarily a great indication of the way people would have spoken at home with their family and friends.

In any language and any era, you'll likely find some significant linguistic variation based on register. That is, just as today we have "how are you" and "what's up", similar contrasts existed in older forms of English (just look up "1800s slang" for some examples).

Sometimes a form that used to be just the normal way of saying things becomes over time restricted to more formal situations. My research is on Romance languages, so I know better examples with that than with English. In French, "I don't know" used to be Je ne sais pas. Nowadays, the ne is usually left out in casual speech: Je sais pas, but you still hear the ne sometimes if the style is more formal. Source. Although I don't know as much about English, I think a similar example might be the use of contractions: "I do not know" vs "I don't know".

However, it's not automatic that the regular, casual speech of yesterday becomes the formal speech of today. Sometimes words or phrases simply die out, and aren't used in any situation, formal or informal. Nobody still says "bully" the way that Teddy Roosevelt did. Other times, a previously standard form can become restricted to a particular type of usage, but not necessarily formal situations. Again, in my area of expertise of French, the simple past tense (Je fus instead of J'ai été for "I was") used to be totally normal, but now it's restricted to literature. So some writers are still publishing books where they use that tense, but it's never really used in speech, even if it's a very formal situation. Another example from English is the thee/thou/thy/thine form of "you". Those words are still used in some Christian religious traditions as part of the language of prayer (due to influence from the King James version of the Bible). But they are not used in formal situations in general.

Maybe someone else can provide more quantitative data on how much of the language restricted to formal registers today used to be informal. My intuition, although I don't know for sure if this is true in English, is that today's formal language is derived from yesterday's formal language for the most part, and changes very slowly, while informal language changes much more rapidly. So 100 years ago, the slang was very different but the polite forms would still be pretty recognizable.

Doug Biber has written a lot about register variation, and I see that this book of his has a chapter about variation over time, but I haven't read it.

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