Apple certified repair made my iPhone worse and now they want me to pay

Hi All, I'm from England.

A few days ago my out-of-warranty iPhone 15 Pro had a screen fault - bottom half completely white, but otherwise working fine. Took it to an Apple-certified store for a screen replacement. They couldn't get the new screen to work, and now my phone has a new issue — it shuts down randomly, which never happened before.

They're saying that it's a logic board issue which is the issue preventing their screen replacement from working and it's also causing the shut downs, but from my POV, the phone only started shutting down after they tried to repair the screen?

They admit they can't fix it and will get me a replacement device, but still want me to pay the screen replacement fee and they they're 'saving me money as l'm getting a new phone for the price of a screen replacement.

Shouldn't a repair-related fault be fixed at their expense? Anyone dealt with this before and got Apple to waive the charge?