This is tough, but here’s my hack:
buy a sheet of sheet-foam/insulation.
Cut it in half and prepare to glue it with a glue that won’t melt it.
Trace your mirror onto the foam and then extend the cut 3” beyond it, or whatever your desired frame size is.
paint it with latex primer and latex paint
Plywood. Cut smaller than the mirror, using mirror for a pattern. If the mirror is not to large use construction glue on the back about and inch all around. Loctite makes one called power grip. If it is larger you could use mirror hangers which are plastic or metal L shaped brackets that fit over the edge of the mirror. One part has a hole that you attach to the wood with a screw and the other side of the L holds the mirror onto the wood.
I love this round mirror frame! She gives you all the instructions to build one yourself, provided you have a few tools!
For a boat design bathroom I used 1/2 inch smooth rope braided tightly, glued to the mirror. It is also cute for chair rails.
you could use beautiful ribbon or trim.