" I was going to put a faux frame around it."

Hold a piece of paper up to the glass. You can see the back of the paper reflected in the mirror because the silver surface is behind the glass. If that doesn't bother you, then I suppose you can glue pieces of wood to the glass to give the illusion of a frame though the "frame" also cannot extend beyond the edges of the mirror because the mirror is jammed against the walls and backsplash.

Are you going to move the vanity light electrical boxes upward? Those lights are going to hang over the mirror and would hang over the glued-on frame as well.

A frame will make it appear dated.

I don't know how you function without medicine cabinets

Replace the light fixtures

This cabinet can be hung behind the door for storage

These narrow medicine cabinets can be recessed between studs on the sides of your vanity.

Here is an example where they used 1” x 4” lumber:

https://livingwithlady.com/2018/05/diy-bathroom-mirror-frame.html

A brutal solution. Are you doing Farmhouse style?

I would skip the frame idea and have nicer down lighting above. Consider glass shades that are either frosted or seedy glass. The clear glass no matter where requires regular cleaning. Once all that wallpaper is removed and the room painted you can have some artwork in there for pizzaz and these will draw attention better.

A frame (especially if adding a separation) can feel heavy and lean more traditional. It comes down to a preference and how you want bathroom to look overall.

I’d leave as is, or at least only decicide once bathroom is complete, ie: this feels lighter and fresher.

Also suggest a bit more interesting lighting

Thanks for the feedback and ideas. As recommended I’ll wait to see the after painted look and decide. I’ll reconsider the lighting fixture chosen.

I have done the same thing - applying painted wood trim to wall mirrors. Here's something I learned since the wood had to be glued onto the mirror. Be sure to paint the back side of the trim. Otherwise, you will see a small sliver of wood reflected in the mirror.

Good point. What was the width of the trim relative to size of the mirror ?

The majority of the comments so far are voting against a wood frame. I believe in avoiding work whenever possible, so skip it. There doesn't seem to be consensus that this would be an improvement. If it were me I would definitely remove the mirror to install medicine cabinets and different light fixtures. For me this would be worth the effort. The mirror could be glued on, so it could be difficult to remove it, but medicine cabinets are much more functional and attractive.

Preview of colors being used. This is another bathroom upstairs where the wallpaper was removed and cabinets painted. For a transitional look I am using matte black hardware, black/nickel vanity lights Frame or frameless mirror ?

A pretty light and no frame on either one.

Frameless it is given inputs received and easier!
I’ll share updates - I hope to find a good vanity light.

Depending on interest and budget, it could be transformed and given the size of your mirror, it shouldn’t be too hard to remove.

Leave the mirror as is I sure hope the wall paper is gone and IMO that Edison bulb lighting is always an awful type of light in any space and for sure in a bathroom. We have never had medicine cabinets in out last 3 homes no big deal good vanity storage works great .

I would not frame the first bath as the mirror seems to run wall to wall - but I would def frame the mirror in the 2nd bath since it is smaller than the width of the vanity and seems less finished

I am thinking similarly.

Consider a thinner frame and thought this article showed a nicer alternative than wood (and method is easier)

https://simplymadebyerin.com/2023/09/28/how-i-updated-my-builder-grade-mirrors/