@videogame95 - I normally put a travel power strip inside the frame for the mirror. I’ve since started adding external switches that cut the power to the power strip, but you can get by with just using the power strip’s plug.
Once you have the power strip in the frame, you can plug in the 3.1 amp adapter into the strip, along with the monitor, LED supply or whatever else you have back there. With some careful shopping, you might find a strip with a USB C plug built into it.