Okay I'll narrow the question down to the Old, Middle and New Kingdoms -- from 2700 to 1100 BC, give or take. Before the Old Kingdom is "pre-Dynastic" Egypt -- not yet a united kingdom -- and after the New Kingdom comes the Third Intermediate and Late periods, when Egypt was mostly ruled by foreigners.

So, technology advanced a lot! Most obviously, the Old and Middle Kingdoms were Bronze Age, while the transition to the Iron Age began well before the end of the New Kingdom. So, the late New Kingdom and the Late Period had iron tools and weapons, and much more access to metal generally. This shows up in the archaeology as iron nails, knifes, fasteners, buckles, and whatnot -- not as dramatic as iron swords, but definitely making a difference to everyday life.

(There's debate over how far the New Kingdom got into the Iron Age before things fell apart, because it's not clear how much the late New Kingdom Egyptians were mining and smelting iron, as opposed to importing it. Smelting doesn't show up clearly in the record until well into the Third Intermediate Period, after the New Kingdom had already collapsed. But New Kingdom Egypt definitely had ironworking, even if they had to import the iron.)

The Old and Middle Kingdoms didn't have horses. The horse first shows up in Egypt around 1750 BC, give or take, but horses don't seem to be widely used until well into the New Kingdom. When you see Egyptians in chariots? That's New Kingdom only.

The Old Kingdom only used scratch plows, afawct. Oxen-drawn plows with a bronze share don't appear until the Middle Kingdom. It's debated how widely they were used, but they would have represented a significant bump to agricultural productivity.

Papyrus is associated indelibly with ancient Egypt, but afawct it wasn't invented until well into the Old Kingdom -- the first few dynasties don't seem to have had it. Interestingly, the potter's wheel shows up around the same time. Wheels don't seem to be used in transport until around the end of the Old Kingdom, though.

-- I use language like "afawct" and "don't seem" because when you're talking about stuff from literally thousands of years ago, the record's not exactly complete -- especially when dealing with evidence that is perishable, like papyrus or fabric. Sometimes things survive; other times, the Egyptians went to the trouble of recording stuff, which is a great help. So, no bread or beer survives from the Old Kingdom, but we have bas-reliefs showing how bread was made, inscriptions that mention beer, etc.

Let's see, what else. Aside from horses, Egypt had a pretty complete package of domestic animals -- donkey, pig, cow, goat, sheep, dog -- from very early, pre-Dynastic times. On the other hand, although we associate ancient Egypt with cats, cats don't seem to have been domesticated until the Middle Kingdom. We don't find depictions of domesticated cats (or remains of them) in Old Kingdom sites. Chickens are another late arrival; they don't appear until late in the New Kingdom, where they seem to have been used more for eggs than for meat. And while the Egyptians of course knew about camels, domesticated camels don't seem to have arrived in Egypt until the Late Period, when they seem to have been imported from the Middle East or the Levant.

There was a steady movement of new crops from the rest of the world into Egypt. Olives seem to have arrived in the late Middle Kingdom, for instance, and cotton around the same time. (Cotton wouldn't become important for a long time, though; the Egyptians mostly used flax.) Pomegranates show up a bit later, in the New Kingdom.

Oh, and one Middle Kingdom innovation that is very much still around today: knitting. This is still a controversial topic, but as far as anyone can tell, knitting was invented in Ancient Egypt and gradually spread outwards from there.

Mind, some technologies may have been slow to spread. The Egyptians knew about glass for a long time -- they imported glass beads and ornaments from outside for many centuries. But local glass production doesn't show up in the record until the New Kingdom. Were the Egyptians really very slow to adopt this technology, or is it just that the record is incomplete? Similarly, the Middle and Late Kingdom Egyptians must have been aware of the arch -- it was used in the Middle East from the middle Bronze Age onwards -- but they carried on with post-and-lintel construction. (To be fair, nobody really grabbed the arch and ran with it until the Romans.)

Mathematics advanced from simple arithmetic and basic geometry to much more complex stuff, including three dimensional geometry and trigonometry. A fun bit of trivia: it appears that by the Middle Kingdom, the Egyptians had an approximate figure for pi. They apparently defined it as "take 4/3, square it, then square it again". That gives 4/3 to the fourth power, which is about 3.16, which is about half a percent off from the actual value.

There were considerable advances in ship design and construction, but I'm not qualified to talk about that. All I can say is that by the late New Kingdom the Egyptians could build large blue-water seagoing vessels, including a no-kidding navy -- and that these things apparently involved technologies that the Old and Middle Kingdom didn't have.

Are these the sorts of things you're looking for?

(BTW, there is a subreddit for Ancient Egypt, and they seem to have some experts there. Pretty sure you can get more detail there if you want it.)

u/Malaquisto has provided two answers to your question, one good, one more problematic, and as an expert I’d like to fill in some of the gaps and talk about general issues with this question.

You’re correct that, from a very broad point of view, ‘technological advancements’ do appear to stratify cultures. Nowhere is this more apparent than in histories of predynastic Egypt, which tend to be based on the theory that developments in ceramics correspond to advances in society (this theory was largely propagated by Petrie). So we describe Tasian and Badarian cultures, and then Naqada culture – only it turns out that you can subdivide Naqada, so now we also have Naqada I, Naqada II, Naqada III. There’s obviously some truth to associating certain methods of pottery making with certain people, but it is I think overused to stratify history. It depends on a view of history in which there was little continuum, and in which everything can be divided into nice little periods – this has very little basis in reality. No culture instantly turns into another – there’s a broad spectrum on which people lie. As a modern parallel, think about how the ‘generations’ are portrayed in the media as these monolithic groups (Gen X, millennials, Gen Z), despite there being considerable similarities between them and differences within them. Concepts like this might be somewhat useful for generalised statements and narratives, but they’re actually often unhelpful in terms of assessing and understanding how people live and have lived.

At any rate, there’s a general issue with the idea of ‘technological advancement’, which is that it presupposes a very linear, always progressing model of history. Brent Shaw has written a fantastic article arguing why this model simply doesn’t apply to the ancient world (he focuses on the Greeks and Romans, but touches on Egypt and I think his conclusion works there). For us, the future is this great expanse in which we can constantly develop new technologies in order to optimise human life/the economy. Everyone is planning for everything; people save money at interest so that it will constantly grow for the future; countries borrow against their future income safe in the knowledge that their income will grow (because they will develop new technology) and they will be able to pay it back and borrow more and pay that back and so on.

This doesn’t work for the Egyptians (or the Greeks or Romans). The future was not something that you really looked at or thought about – the people who did do this were gods and oracles, who would give you advice but wouldn’t tell you exactly what could happen and were often dangerous. Indeed, while we always view the future as being in front of us, for the Greeks and Egyptians the future was often perceived as being behind us: we can, after all, see the past, but we cannot see the future. The Egyptian conquest of Nubia in the New Kingdom is a useful case study: there’s lots of good reasons to conquer Nubia, both in terms of materials and ideology. But there’s no sense that the Egyptians planned for years to make this conquest happen, building up an army and fortifying settlements, establishing supply chains etc. A power vacuum opened up and Thutmose I immediately filled it. And then when Egypt did occupy Nubia, Upper Nubia was left under indirect control without any effort made to properly annex it (the opposite of what we see with Russia and Ukraine today, for example). Any action was fundamentally reactive: the invasion happened primarily due to revenge and the need for plunder/wealth extraction; fortresses were constructed in distinct temporal stages rather than under constant redevelopment, and in response to a threat.

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