I’ve had 4 pixel watches now. The first 3 were the first gen and every one of them did this. They replaced the first 2 under warranty before the 3rd one ran out of the warranty. The 4th one is the current Gen watch. I really didn’t want to buy another one given how the first Gen went, but they are the only ones with the hourly activity reminders that actually make sense (imo) out of everyone (other than apple, but I have an android so I’m not paying for a watch I basically can’t use).
If your watch is still in (or even close) to the warranty, they were pretty good about replacing it.
From what I could figure out, it seems like the glue they are/were using to keep the screen in place isn’t that good. Whether it’s weakening from the heat or the watch or general movement or what, it’s not if it comes apart but when. Now those were the older generations, but it doesn’t seem like too much has changed design wise in that time…
I never had a problem with the battery but that could be because they never lasted long enough or you got unlucky, I honestly couldn’t say. I think your biggest thing for replacing the battery is just going to be about getting that screen to actually stick in place once you’re done.