Need help diagnosing if there is a leak in my shower threshold
The best way to confirm if your shower basin has leaks around the tile is to plug the drain. Remove the grate and install a stopper of the appropriate diameter. It must be 100% plugged. Next fill the basin with water. It is easier to use 5 gallon buckets filled from another water source. Fill the basin to just below the curb. Mark the water height with tape and/or marker.
Wait awhile and check if the water level has dropped. If it hasn't let it stay over night and recheck. If no noticeable change in water level there are no leaks in the grout or joints.
I would suggest re-grouting those joints that have missing grout and any others that have loose grout.