I'll second that Thimbleweed Park suggestion!
A couple of others that jump straight to mind that you might want to look at are primarily Disco Elysium and also maybe This is the Police that fit into both categories.
Also, the Monkey Island games are still around if wanted to relive those (and there's a new Indiana Jones game on the way, though it's some way off!).
For some similar point-and-click storytelling, the Life is Strange series is good, as are most things by Telltale Games (The Wolf Among Us being another good-sounding fit for your tastes). Recently I really enjoyed Unpacking as an all-too-brief distraction, while Gone Home is a slightly older game that tells a good slow-burning story.
Also off the top of my head, there's an old Xbox One game called Murdered: Soul Suspect that has you playing as a dead detective investigating his own death (in a non-shooty environment) that could be worth looking into. Or at least I seem to have enjoyed it more than most anyway...
