I am going to assume you have run the shower and watched the water leaking from that spot, eliminating any other possibility like water following the grout lines on the outside.
Redoing the grout may stop the leak from exiting, but the problem is water getting back there and coming out the grout. Closing off the exit just means the water will go elsewhere.
I would start with removing the glass and sealing the screw holes that may have compromised the waterproofing. You might as well seal the glass trim as well, both under and around. While you are at it remove and reseal the caulking around the shower pan. I would not reseal the grout unless the above resolved the leak.
If you have access below the shower, I would look there even if it means cutting a hole in the ceiling. That may give you a better idea of where water is actually entering behind the tile and if it is getting anywhere else. Doing a drywall patch is better than not knowing if water is getting elsewhere.
The best thing would be to remove the glass and tile to really understand the source of the problem. You may end up having to do that to fix the problem if resealing the screw holes and pan don’t resolve it. Long-term you would want to redo it anyways because there has been a waterproofing failure and that should be properly fixed. If you end up ripping out the tile, you can use inset glass track that won’t puncture the waterproofing and will likely need new glass made.