How do I cover a large opening in a loft for privacy?

Room divider or screen, or you can hang a curtain from the ceiling. Drop cloths are perfect for this.

I agree with Naomie

You could use curtains attached to a rod and slide those open or closed depending on what you want at the time. They could match you front room curtains so the looks is more consistent and coordinated.

Do you want the cover on the open part of the loft to be permanent or something that you can open and close?

I've lived in 3 lofts in my life.... for privacy and to define rooms we have had free-standing walls made, I have always used tall bookcases for both storage and to seperate sleep areas. I've also had a steel cable strung across an area to hide the kitchenette.

The bookcase I see used the most is the Ikea Kallax open bookcase.... https://www.ikea.com/us/en/search/products/?q=room%20divider%20shelves

You can put fabric or basket cubes on it for storage to to make the wall more private. You can also add a fabric backing to it.

When adding a free-standing bookcase or wall in the middle of a room, you usually screw it into the floor, and/or run steel cables and eyebolts to secure it to the ceiling/beam to prevent tip-overs.