Chosen Solution

Home button is faulty, More often doesn’t work, but Touch ID does. I tried changing the screen, completely, flex cables as well, but nothing. Tried with a new home button, same issue. Don’t know anymore what to try to make it work. Ideas?

From what I can gather is that the fingerprint circuit is all okay. That tells me your menu key connection is faulty. There is not a lot on that circuit and I would suspect either a faulty connector or a nudged component. There is one diode and one resistor sitting close to the connector if one has been accidently pried it would result in the “no return function”  You will need a multimeter to test them. Test in continuity mode first then check OHM’s mode across the resistor with a known good board.

Sounds like a torn home button flex. No much you can do but replace the button and lose Touch ID and keep home button functionaly.