16*2 1602A LCD not displaying any character or contrast, although correct wiring
Ok so the problem were the wires.
Although I tested every single wire for continuity I went to the store and bought a brand new (expensive/not-from-aliexpress) pack of jumper wires. I rewired the entire project with the schematic and code that was posted in my question-post and it worked like a charm..

So I'm not sure what exactly caused the problem, but it was in the wire. I thought having continuity in a wire is like a 100% proof that the wire works properly. Maybe someone has an idea what could cause this?

So again, I only replaced the wires, not the schematic nor the code, with brand new ones and it worked perfectly.