As someone who hasn't played Aurora since one of the earlier VB versions, has not touched C# version, and does not have the patience to go through the massive changelogs...
I'm diving into C# today. Anything big I should know or look out for, or can I mostly proceed as I used to and feel out the changes?
Oh boy, there's a lot, but a lot of it is also small changes that just make the game better, QOL and stuff. In terms of things you actually need to know, er..
Someone already touched on maintenance, but maintenance is also very different in terms of how capacity works. VB6 had this strange mechanic where your maintenance facilities increased the "max ship size" that could be maintained, but you could have as many ships as you wanted below this. That and fighters weren't serviced by maintenance facilities, as a sort of balance against just fighter spam to take advantage of that.
Now maintenance is by total ship tonnage at a location, so it's not just how big your ships are but how many of them you have. As a consequence, fighters are also maintained now since fighter spam will eat into that capacity.
Admin commands change things up a lot too. You used to be able to describe a hierarchy for your navy but this was more for RP or fighter organization than anything. Now we have actual admin commands that you use to structure and group your navies. They replace fleets and are different in the sense that you don't have like, 8 staff officers per fleet, but rather just one commander and the staff officers are abstracted (although that would be cool to see again). Admirals and such give their bonuses through admin commands, which are augmented depending on what kind of admin command it is, and you can nest multiple admin commands to get multiple bonuses from flag officers (although with very diminishing returns).
Er.. there's some big QOL stuff with being able to double click locations now to get the most common order for that (e.g, double click a planet to get a move order). PDCs are a thing of the past and are integrated with ground-force design, and you build units call STOs instead (surface-to-orbital guns). There's also some cool stuff with fighters and loadin/unloading mechanics where ships below 1000 size can land on planets and don't need shuttle bays or spaceports, and there's a whole class of weapons for fighters now that you can use to turn fighters into pure ground support units, but you can also use space fighters, they're just less efficient and less specialized for the task.
Lots of cool stuff, but it mostly just feels like Aurora but better. And faster. There's a thread with a full directory of changes, it's pretty long but is good for some reading material if you get bored.