This picture doesn’t express why a door can’t work. I see a rectangular opening, doors come in many sizes and can be trimmed if needed. Maybe more pictures would help?

Hoping this photo helps demonstrate the angle issue.

A heavy full length curtain? It could be drawn across, from either side, and to keep it from gaping with some strategically place magnets or magnetic strips?

See if a blind hinge will work - - its designed to accommodate non 90 degree angles -usually applicable for cabinets

Frame and drywall the left angled jamb to parallel with the right.