Escutcheon plate doesn't cover hole in tiled shower wall
I have run into this several times, the least expensive method I have found is to remove the plate and use grout, epoxy grout in this case I can’t tell if there is backing but hot glue on a paint stir stick really works , any epoxy that is fast setting could also hold something in place. Then fill with the appropriate color (white in this case) grout. I like the epoxy grout for things like this because it seals better.
You might say the color will be off as new grout even from the same bag will look different but in a small area like that the fixture changes the look also. In a few months it will look about the same and is not noticed by most unless they do this type of work.