A thicker battery would need a new back built with a hump or standoffs across the whole back to increase the overall thickness to match the new larger battery thickness...
Correct. This used to be done before on flip phones, and is still currently being done for dedicated cameras.
This is a solved problem and not an issue.
I've had a HTC HD2 that had exactly that[1] - an extended battery with a bump. It looked silly, but did its job and in daily usage wasn't that big of a deal, actually provided a resting spot for my index finger.
[1] https://www.phonearena.com/news/Extended-battery-with-kick-s...