I have desperately been looking for software where I can:

Build an opening repertoire from PGNs.

Drill that using spaced repetition (like Chessable)

Import all my games from Lichess and Chess.com

Tell me when I deviate from my repertoire in those games.

Do you know of a software or combo that can achieve that?

I really like Listudy for drills, it imports from Lichess studies (which you can create from PGNs):

https://listudy.org/

Also Opening Tree for bulk analysis:

https://www.openingtree.com/

They're both free and open source.

Opening Tree is great and I use it a lot but it does not persist my games - I have to download them every time I use it. But I'd love an app with that interface that could persist the data and cross-check it with my repertoire. I guess it would not have to be same tool as the repertoire trainer, it just seems cleaner to have it all in one tool. But you are right Listudy can help with the spaced repetition, it just doesn't know anything about my games :)

I'm currently developing this: https://www.chessmonitor.com/

It stores your games and gives you an explorer for your games similar to what openingtree does.

Here is an example for the current world champion: https://www.chessmonitor.com/u/kcc58R9eeGY09ey5Rmoj/explorer

Wow that is awesome! Great work!

Opening Tree also is opensource, you could modify it to run on local data and then build and run it on your computer:

https://github.com/openingtree/openingtree

aside from working offline (which is important!), what are the advantages over an online tool like lichess?

Have you tried ChessX, and if so, how would you say it compares?