The floor of the tub in the Tsar's bath would have been flat. The depth of those kinds of tubs was approx. three & one-half or four feet.
There is usually a seat at one end so that you can sit down, with your head above the water.
Yes, Londo, you are correct, the bathroom of the Tsar was done up Turkish style. It was like entering another world.
Turkish baths were the rage in those days so I am sure the Tsar thought the whole affair was most up to date.
Douglas