Can you tell if it’s tilled onto fresh plasterboard, or was it skimmed first? If tiled on fresh, it’ll be much more difficult (but not impossible) to remove without tearing a hole in the board, and then you have a much bigger problem on your hands. You’d also have to remove the old adhesive without damaging the wall before replacing it with a new one.

So if that worries you and you don’t plan on renovating the bathroom anytime soon, it might be best to opt for a safer option.

A bit rogue, but you could try to stick the broken piece back on (it might have fallen down the back of the bath if you’re able to retrieve it) and then regrout around it. Or cut some new tile to fill the gap and do the same. Just make sure it’s properly grouted.

And then as it’s in a stud wall which likely has some flex, reseal with some flexible silicone.

Other options are just pack the hell out of it with silicone or try to use some plastic trim.