I'd say, scrape out as much old grout/sealant as you can. Clean it really well and apply a new sealant. If it doesn't work, demo is in your future.

Also, there is likely more damage under it all from the water. If it were me, I'd tear it out and redo it properly.

If that's actually an open corner (no waterproofing/pan liner behind it & up the sides behind the tile 6-12"+) caulking is not going to keep it from leaking.

Demo & redo enough of the bottom section (and curb) to make sure there are no future issues.

Luckily the damage underneath is minor, as I was able to confirm form cutting through the living room ceiling. I’ll fill in the gaps with grout and apply fresh sealant, hopefully that should do the trick.

It definitely doesn’t seem like it’s up the sides, otherwise there shouldn’t be a leak correct?

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It's easy enough to fold/cut the corner of the liner wrong, or poke it during install if you aren't careful. Cut a hole in the ceiling to keep the leak exposed, and see how long the temp solutions actually keep it dry.