As an 80s baby I grew up playing Sierra games on PC and one series my brother and I would play a lot was the Police Quest series (along with Space Quest). I found a website where you could play Sierra games (first one I played was Leisure Suit Larry since I wasn't allowed to play it as a kid) and I am considering doing a replay of the Police Quest games and basically a total retro gaming dive until Starfield and Elder Scrolls 6 comes out (my main gaming at the moment is Modded Skyrim, Sims, and Assassin's Creed Valhalla).
Can anyone recommend any good cop games whether old or new?
Not really cop games, since they're cyberpunk, but you can look into the Shadowrun games since you like RPGs (Returns, Dragonfall & Hong Kong) (Returns is the worst, DF the best).
I really enjoyed playing DF & HK.
Adventures with a cop theme might be Gibbous (Cthulhu/noir adventure with a humorous (!!) take) or Cognition: Erica Reed.
They're not the best you can play but I had fun with both of those games.
Regarding adventures in general (since you liked the *Quest games):
Gabriel Knight, King's Quest and all (old) Lucas Arts games (Monkey Island, Indiana Jones, Loom, ...)
Thanks!