Could they have been used for hanging clothing hooks? Such as night clothing PJ’s etc or day clothing? If, or maybe it’s when, you remove them, you’ll learn if they are secured with molly bolts etc to make them more secure & able to hold weight. What’s the doorway next to them lead to? Definitely a puzzle.

They look like drapery holdbacks but maybe they had pictures hanging from them or something?

Def not clothing hooks — a few are quite high. I agree that they look like drapery holdbacks, and if there were two, one on each side of a doorway or window, that is what I’d assume they were. Could’ve had pictures hanging from them, except that there is one right by the door frame that is the entrance/exit from the room. There couldn’t have been a picture hanging from that.

I think @palimpsest is correct that they look like drapery holdbacks. I’d been thinking cabinet or drawer hardware but now I’m thinking they are larger than I first thought. Spacing doesn’t seem right for art hangers. Are the sale listing photos still out there somewhere? Maybe they’re shown there. Maybe a call to the sellers realtor through your realtor? A lot of effort but it’s just such a puzzle!

Probably to turn scarves, necklaces or favored outfits into wall decor.

Whatever the purpose, they're nonessential. Remove them and patch.

They are fancy wall hooks. The PO most likely have them spaced perfectly for their use.