The second picture shows the grout cracking, probably from poor support and resulting movement. I see a tear out and total rebuild in your future.

I agree with HU-867564120 that movement is causing the grout to separate. I’m thinking this been an ongoing problem and the previous home owner used caulking to try to seal the floor. The caulking is dissolving and that’s the “cement” looking substance that you’re having issues with.
I agree it’s definitely in need of a rebuild.

It looks like maybe the cracked grout is letting water behind the tiles and dissolving whatever was used to adhere the tiles causing it to seep out- maybe something that was not the proper product. Is it weeping from both the glass wall tile and the floor tile?

I agree with the others. That water is going somewhere. You need to check carefully to see if the shower has sprung a leak.

I see a leak in that shower for sure this needs a redo there is no way to fix that mess . Rip it out now before some real damge is done.

Sorry you have this problem but as others have said, this should be ripped out ASAP to avoid more water damage.

It looks like the floor is uneven and the cracked grout is often due to movement in the substrate. Is the "stuff" on the drain smooth or does it feel like it has sand in it? It also looks like there is something happening to the lower rows of grey wall tile. I think you need to carefully remove a few tiles from around the drain and see what's happening.

This is more than a grout problem Terso. Stop giving misinformation

Mr Terso, please stop with the misinformation.

@cpartist, you are probably right as nothing can be properly evaluated based on pictures, it’s always best to have a professional on site to properly access the materials or damages to issue an accurate solution. Better to have an expert properly evaluate the shower that is the best opinion.