You can get a keyhole hanging plate that you just have to chisel away (or drill) some room for the screw head that you have in the wall to recess into it when you hang it. You could put on on either side at the same height or the very center, if you’re confident about that it will hang level.
Keyhole Hangers, Single Hole Hanging Plates - Pack of 25 - by Woodpeckers Crafts https://www.amazon.com/dp/B06VY1R2QV/ref=cm_sw_r_cp_api_UTBoAb1E3ND3T