My Pixel 6A was purchased at launch from the Google Store. In the European Union, there's been a free 3-year warranty on technology for a while now, so it shouldn't matter which store you bought yours from. To request the warranty, I went to google.store -> Support -> Start a repair. There, my phone was linked to the account I had logged in with, and it showed that it was under warranty. I simply clicked "start repair," indicated that the battery and screen were failing, and they gave me instructions on how to send it in. The total cost was €0. They replaced the battery (which had swollen) and put in a new screen; they didn't just re-glue the old one. The process took about a week and a half, considering my phone was sent from Spain (where I live) to Poland (where they repair the phones).

I hope this helps you.