Looking at that the grey bit in the centre probably contains the anti odour flap and that is I’m guessing gummed up and not letting the water out due to scuzz and hair. You could try putting some dishwasher soap down it and leaving overnight. It eats scuzz very well. If that doesn’t work I’d drill a small hole (small enough that a self tapper with a rubber washer will seal the hole in case it’s the bottom of the trap) in the grey bit and have a poke around with a pick. If that fails it’s a hole in the ceiling underneath it I’m afraid. Possible easier and cheaper than touching the shower floor.
Looking at that the grey bit in the centre probably contains the anti odour flap and that is I’m guessing gummed up and not letting the water out due to scuzz and hair. You could try putting some dishwasher soap down it and leaving overnight. It eats scuzz very well. If that doesn’t work I’d drill a small hole (small enough that a self tapper with a rubber washer will seal the hole in case it’s the bottom of the trap) in the grey bit and have a poke around with a pick. If that fails it’s a hole in the ceiling underneath it I’m afraid. Possible easier and cheaper than touching the shower floor.