I could not get a replacement as I bought the phone in a foreign country (Google doesn’t sell Pixels here in Brazil).
So as much as I love the idea of running a more private phone, I found the hardware extremely fragile and poorly designed, so I will not buy from them again anytime soon.
This sounds like your phone may have been one of the Pixel 6a models with a defective battery[1]. It was a major problem for which Google pushed out an update that nerfed the battery life. There is a tool online where you can check if your particular 6a was one with a battery from the bad production batch[2].
But that unfortunately doesn't help if you are in Brazil where, as you say, Pixels aren't officially sold and import/export controls tend to make tech warranties useless in practice.
[1] https://www.lifewire.com/pixel-6a-battery-overheating-warnin...
[2] https://support.google.com/pixelphone/answer/16340779?hl=en
The flag ship should not be more than $500
Which is (almost) the case during sales. The P10 was on sale for $599 not long ago, and you could buy a 9a for little more than $300. That is extremely good value compared to any iThing repoted your every move to Apple.