There is a crack. This is normal and expected, because grout doesn't flex. Every time someone gets into the tub, the tub will flex a small amount, and that will crack the grout. Then water gets under it, and problems start.
That's why the joints around the tub, and usually in the corner of the shower, have to be done with silicone caulk and not cementitious grout.
However a silicone caulk joint needs to be wide enough to stretch. The idea is that, if you fill a 1mm wide crack with silicone, and when you step in the tub the crack enlarges by another millimeter, that will stretch the silicone from 1mm to 2mm, or by 100%, so it will tear. But if the silicone joint is at least 5mm wide, then the stretching is a much smaller proportion of that, so it doesn't tear.
So you need to remove the cementitious grout along these joints first. You can use a scraper, a painter's tool, whatever works.
Then you need a tool like this to apply the silicone:
Basically if you use your finger, you'll push the caulk into the joint and make it "hollow" (right) and it won't last. If you use the proper tool, the caulk will cover the top of the tile over a few mm (red arrow) and it will have much better adhesion.
