Why my phone doesn't open completely?

crap inside hinge

slide post-it sticky side inside hinge through gap to try to get all dirt/hair/dust out, go slow, do it a lot

or disassemble phone and use toothbrush inside hinge

samsung repair/care/whatever is a scam, don't listen to them they're incompetent and will overcharge you

there are even cases where they bill replacements that they don't do (for example in your case they'd bill you a screen but they'd only clean the hinge like I suggested)