I have 2 IKEA mirror cabinets for sale. $100 each.
They are an earlier version of the IKEA Godmorgon Mirror Cabinet with 2 doors:
https://www.ikea.com/ca/en/catalog/products/10218999/
Each is 27.5" wide x 37.5" tall x 5.5" deep
Glass shelves, mirrored surface on inside of door and along the back of the cabinet interior.
In Very Good condition!
We had installed them next to each other to make a large mirror, but you could install just one in a smaller bathroom.