Wall cladding in the bathroom

ok, if I understand correctly, your concern is to smooth the currently built interior walls?

The goal should be tiled walls or painted plaster?
Isn't your question already answered by this?
-> plaster all walls, and tile over where you want. In my opinion, this is the simplest and highest quality option.
just make sure to use materials suitable for wet rooms

I see no need for any kind of engineered boards here

And if you only have the bathroom plastered separately, I would consider lime-cement plaster as an alternative to gypsum plaster. In my opinion, it is still a bit more valuable for a "Feuchtraum".

After gutting our bathroom, the walls present a "terrible" picture.

No, that is a completely normal sight. Walls with plaster and tiles knocked off always look like that. Rougher than the raw construction before the first plaster, yes. But nothing has become uneven there. I see no drama in that.