Is Applecare purchased in the UK valid in Italy

Hi - I have an AppleCare package for my iPhone XS Max. I have cracked the back and slightly bent the metal sides - the screen, thankfully, is fine. I bought the phone and AppleCare in the UK, but now I am in Italy, and wanted to know if the AppleCare can be used at a store in Italy?

Also, I am trying to weigh up if the cost of the repair is worthwhile, vs the trade in price of the slightly damaged phone - the cost is £79 unless they treat it as a screen and charge £25. Of course I might get a new phone...or just leave it, accept the lower trade in and wait for the 12 to come out!

All thoughts helpful!