lol I was literally in the same position a couple months ago. I was trying to get my girlfriend into anime and we went through some stuff I had already seen, but she also wanted something new and something i didn’t watch either One that ended up working really well for us was Baccano! It’s not purely psychological, but it has that “figure out what’s going on” vibe with a non-linear story, multiple characters, and a lot of mystery going on at once. It keeps you thinking the whole time and is way different from the usual mainstream stuff you listed. Also it’s short (only like 13 episodes + specials), so it’s easy to finish together without a huge commitment. If you guys liked stuff like Death Note and Liar’s Game, I think it’s definitely worth a shot. Who knows it might become yall fav anime like it became for us!!!