My first reaction on seeing the title was to name a games that just have fun core mechanics where replaying the game is basically just doing more of the same fun thing, so ULTRAKILL means I’m on the right track.
Prodeus is a pretty good doom clone. Not as in-depth as ULTRAKILL, but nonetheless has fun weapons and your basic doom (eternal) movement/mechanics. Blasting your way through enemies is as fun on the first level as the last. And the Quake games hold up extremely well, and the mechanics are so simple and powerful that you can really have fun replaying and getting better.
Stealth games are also very fun for this. The Splinter Cell series (especially Chaos Theory) are very fun to try to perfect/improve on. Dishonored and Thief as others have mentioned. And Midnight Club is the best racing series for this. You’ll have to emulate it, but it’s worth it. Completely open-world, and learning the city layout over time is very satisfying.