I haven’t showered in this shower for years, sorry, but you have to assume you come out dirtier than you went in *shudder*.
On the topic: what you can see in the pictures already suggests water damage. There is definitely mold... overall, I would completely redo the bathroom. What you can see is so filthy that you shouldn’t even start cleaning, but rather get rid of the stuff as quickly as possible (I would only enter such a bathroom wearing a full-body condom).
Then check whether the water damage is bigger (do you know the residents below you? You could ask them if they maybe have stains on their ceiling?); depending on that, you will need to get professional help to fix the damage. In a condominium owners’ association, such damage is usually covered by an appropriate insurance, so make sure to inquire!
When the floor is dry again and the structural stability is clarified, you can either tile anew by yourself or hire someone to do it and install a new shower. I would never tile only around the shower here. This seems to be a rather small bathroom; check if you can get leftover tiles at the hardware store. That’s how I once got ridiculously expensive Italian tiles for my kitchen for next to nothing. They are eager to get rid of leftover stock.
And then: clean in the future! It looks like hard water, well, you just have to fight against it. There’s no way around it.
One question remains unanswered here: are you a tenant or an owner? I assume you are the owner, otherwise it would be the landlord’s responsibility.