I've got a shelf for a living room set that I bought third hand in Germany. I want to hang this shelf, but its got strange brackets and I don't know what they're called to look for the respective hardware that actually goes on the wall.

Unsure if this post fits in this community, so I'm sorry in advance if it doesn't 🙏 It's driving me crazy that I can't figure it out

Edit: for reference, the screw on the right is the upward/top side of the shelf