Tub only leaks when filled and plug removed
There's no pressure/overflow inside the walls that would explain this. There is a tub overflow that connects to these same drain lines, and due to their position, they could be partially related to the actual problem.

This indicates the drain lines have a leak, likely a bad glue joint on the top of the drain line near the trap. If there's any partial blockage further down the drain that would worsen this issue. The tub overflow is also connected on the top side of these drain lines, and if it's improperly connected, that would be another example of a bad joint on the top of the drain line.

You'll need to open up the wall or the ceiling below to find and correct this bad drain line.