those are always hard, I would be most concerned with finding something that gets the light past the cabinet.https://www.mirrorsandmarble.com/products/lighted-twin-door-led-bathroom-mirror-medicine-cabinet-36-wide-x-32-tall-flush-mounted-vertical-led-bars-6000-kelvin

Have you looked at the LED lit medicine cabinets? Otherwise, you may have to do an up-facing light about 30 inches wide or a tube style.

how much space is between the bottom of the outlet and the top of the mirror? tape it out in blue tape and see.

The ceilings are 9’ so we have room. I think a tube style might work. What width in that case?

We already got the medicine cabinet so I wouldn’t buy a new one.

No wider than the width of the medicine cabinet. I did a 20" down facing light over a 20" medicine cabinet.

The light hardly projects beyond the cabinet. I was worried about the light (it's the only light in the bathroom) but the light is plenty bright and I generally use the dimmer.)

thats not what I meant tho, or are you able to put the power where ever you want? see the above picture look at the space between power supply and the top of the cabinet. if the cabinet is 35 wide no more than 30 inches.