I am not a pro, but if this were my shower, I would take out the tile to see if there was any mould/damage behind it. So yeah, I think it's a replace both tile and grout job.

Looks pretty old and tired. If you can, have it retiled. By a pro.

Jupiter, this should have been picked up on the inspection and allowances made for replacement. However that's water under the bridge now.
At a guess, there's been water penetration and it's been swelling the wood behind the tiles and resulting in the deformation to the extent that the door doesn't close. As mentioned, it's a do-over. Don't put it off for long. There could be other things lower down getting damaged by the water.

I concur with the others... total gut job

I'm with everyone else. You can tell by the LAYERS of caulking that has cracked and then reapplied; cracked and reapplied; etc that this is a LONG standing issue. Please be aware that the LONGER this issue was allowed to go on like this, the more damage there is BEHIND those tiles.

Tiles don't "pop" off without reason. They pop off for very good reasons like moisture intrusion soaking the wall behind the tile. I would say this has been "fixed" at least 3 times. And the amount of "black mold" showing up looks to be very, very, very old.

You could *possibly do another caulking job on it to get another couple of months...but the longer you wait the more damage you will cause. No matter what you do today, it will be a complete gut job tomorrow. And tomorrow is coming very quickly with this type of damage.

I agree with everyone else. This is a total failure of grout and tile. I'm sure this was never waterproofed correctly and looks like a long standing issue as mentioned. Did you have a home inspection? Was this noted?

Hammer time.