Ascertaining damage from fully discharged android phone

I recently purchased a refurbished Pixel 8 Pro which was supposed to be in "pristine, flawless condition and looks and functions 100% as new". I do have a window of opportunity to return the phone and don't know if this is warranted. Unfortunately when I received the phone it would not start - and I needed to have it on a charger a while before it would actually turn on. After slowly fully charging the phone it appears to work OK, but I don't have an expectation /benchmark to test it against. I did install Acubattery. In slow charging it from about 24-84% it reported a battery capacity of about 5524mAh - however the phone battery is only rated at 5050mAh. (The second charge from 84-100% showed a capacity of only 3312.8 mAh). Battery Guru shows similar result of 100% health. and 5507/5050mAh. **How worried should I be about receiving the phone with a battery that was fully depleted?** - especially if I am planning for keeping it as long as possible. (This phone cost 3 times what should have had to/wanted to spend - but I purchased it because it had a few killer features not available on other phones - particularly the ability to run other ROMs like GrapheneOS and WIFI calling compatible with my carrier and a 7 year support guarantee and the Pixel 8 screen and battery is just too small.)