No frame rectangle would be the best in a tight fit. The rectangle gives you the most usable suface and storage options. I installed a cabinet with a longer mirror. When shut it hides a convenient outlet.

Here are two mirror options that we have used in designs for our clients, perhaps one of them will work for your bathroom:

Logan Townhouse · More Info

Logan Townhouse · More Info

You will need to wait on the light until you know the full depth of the medicine cabinet, also make sure when you mount it there is clearance for the door to open above the light. Also to that point depth will mater to the outlet being completely blocked.

Thank you everyone for contributing your thoughts on this project. Here is an update on the progress:

I would like to paint the vanity cabinet a warm off white like the walls. I asked chat gpt for a rendering. Do you think I should paint the cabinet or leave it alone? (All my cabinetry is honey maple throughout this 2000s era house.)