If it is impossible to put in a pocket door (which we have designed into two of our houses and highly recommend), then consider hanging a sliding barn door on the water closet's interior wall side. You can design the door panel, look for a used door panel, or consider a frosted glass panel or even shutters. Good luck
https://www.houzz.com/magazine/barn-doors-slide-into-style-stsetivw-vs~1622742

Thanks for the response, AD. The space behind the wall has some nice storage cabinets, so the barn door option is out. But that pocket could be an option if there's length enough to the wall to the right. Unfortunately, there's not a whole lot of room in there. The previous homeowners opted for a bigger space in the MB in lieu of closet/bathroom space.

I see a tiny bit of what might be door panel on the left side of the image. Were the panels like "saloon" doors? Not floor to ceiling?
It does not look as if there is enough wall space in the little room to install a barn door in there.
It might be possible to put a floor-to-ceiling bifold door there. Maybe louvered? Maybe frosted glass?

Yes, a pocket door is what you need.

tipi, yes saloon doors. Yee Haw. We are in Fort Worth, you know. Floor to ceiling might be good if I can't fit a pocket.