The Jazz music that plays in most Tex Murphy games, what exact genre is it? I mean, if I want to find (not game related) similar music, where do I even begin?

Great question. Unfortunately, I don't have an answer to the genre question. To start, check out the film score to the french film Ascenseur pour l'échafaud by Miles Davis. Next, you might check out this playlist that calls itself Jazznoir Sampler that spans quite a range of genres but has a few songs that are probably along the lines of what you are looking for.

Just carry a pocket dicta-phone when using corporate and hotel elevators, after few weeks, you should have a respectable collection, lol ;-)

I still get the chills after hearing the chapter openings in UAKM, loved the music enough that I scoured the internet before they were released on GOG as extras.

noir(e) perhaps? Not so much in Tesla Effect... it had more range. One of the levels sounds like Star Wars music from one of the recent films. But I still enjoyed most of the soundtrack for that one.

LA Noire (another game) has a soundtrack you might be interested in. (should find some on youtube)

You should have a blast when you reach the backers credit sequence then ;)

Looking forward to it, now I just need to upgrade my machine so I can actually play the game!