I played through Kotor 1 + 2 for the first time ever almost exactly a year ago. Now, they're among my favorite RPGs ever. I shouldn't be surprised considering BioWare and Obsidian are top-five developers for me.

The Kotor games work so well for me for two reasons: 1) they explore and add context to the Star Wars universe, which you bring up in your post vis-à-vis Mandalorian culture, Sith history, etc. and 2) the games have excellent characters you can interact with in meaningful ways. Those factors are important for me because I always thought what set Star Wars apart was the world and the characters. I suspect that's why I prefer the news Star Wars series over the new movies.

Side note: I did light-side runs. I can never bring myself to do heel/renegade runs in video games.