Sliding door in drywall (interior), tightness

What I do wonder, though, is how soundproof such doors are and possibly how well they protect against moisture from the bathroom?

A sliding door is not just a sliding door. There are systems that meet high requirements for soundproofing and sealing. These are expensive and rare. You solve that with money. Our sliding door to the bathroom is not optimized for the criteria you mentioned. It is wonderfully usable and a design treat. The soundproofing is worse than with a normal door with a door leaf. It is also not sealed against "steam." In the layout of the room in the house and our life situation, this fits perfectly.

We had sliding doors to the bathroom in the holiday apartment. Despite solid construction, they were as soundproof as a curtain.

Used glass or a wooden door?

Wooden door. Running in the wall and even with sealing. Still extremely sound-transmissive compared to a normal door. And you have to like the rolling noise as well. After that, my wife was cured of her idea to install a sliding door to the kitchen.

have you chosen a model by now? We are still looking as well...

still in the concept phase, but leaning towards Knauf Pocket Kit in CW 100 drywall. Door then from the local dealer possibly with additional seals from Fa. Altherm (or similar, I don't have the name handy right now). And you?

Are still in the planning phase. Nothing decided yet. At least [Endlagendämpfer] should be available.