New windshield wipers seem ineffective

My car, a 2004 Opel Astra, has new windshield wipers. Whenever I go to use them (since it’s the start of winter right now) they wipe some water off, but it’s never a "clean" wipe (like a .. residue? on the windshield) and it makes a god-awful screeching noise.

It wipes the entire area that I expect it to wipe, but I have extremely sensitive hearing and moderate tinnitus, which makes this scenario almost impossible for me to drive with.

Is it possible that the windshield got damaged since it was standing for a while (due to broken gearbox)? If so, what steps could I take to fix this? I have Googled for windshield polishing, but honestly I have no idea how to interpret the results, or if that’s even the issue.