The Pixel 6 was one of those awful designs where you have to go in from the front and risk damaging the screen in order to get to the battery, it's no wonder getting it replaced was expensive. That price has to factor in a potential screen replacement if they mess it up. Thankfully later Pixels can be opened from the back instead.
I just got mine replaced on my pixel 6, total cost was $200.
Still gonna hang onto it because there's no reason to replace but yeah labor costs for android are a bit ridiculous.