MacBook Pro doesn’t turn on without charger
Looks like your new battery, from the screenshot above, is only supplying 7.3V, which is presumably too low to power the motherboard sufficiently on its own, it should be closer to 12V.

So your battery might be rated 11.1V but it appears to be faulty, although it is not self-reporting as such, maybe because the mAh rating and cycle count is still ok.