"Will the edge of the tile show?"

Yes. Experiment before tiling please. Schluter may work.

Yes dear, the edge of the tile should show to avoid plainness

Schluter or depending on tile selection there may be a bull nose edge available.

I have tiled around numerous mirrors and the edge of the tile has never shown. The tile just butts up to the mirror.

"the blue will have a overlap of tile on the mirror." What does that mean? Why would there be tile in that corner, and why would tile overlap the mirror?

BIG mistake all around, and everywhere. A classic home JOE LIPSTICK on A PIG effort that won't save any real dollars and will fail.

Get rid of the builder mirror. TATA. Yes, it will be a drywall repair. Simple.What's on the side? Med cabinets?

Go stand back and take better pictures of the existing.

What is the feel in the bath?

What is the inspiration...add that in a picture.

You want the tile at the same level height back and adjacent walls. Or all the way up.....or just a higher riser in same solid surface as counter. I'm feeling the "kludge" before the kludge happens here.......

Bottom line? Stop.

With whatever you were thinking ....... sorry. that's just truth.

The mirror should not be trapped behind the tile edge.

Paint & caulk and forget the tile.

Or reinstall a short backsplash in the counter material like the one you removed.

Or remove the mirror, tile and then reinstall the mirror.

This looks like a very small bathroom and a small vanity. I would keep it simple; adding another element will just add visual clutter, IMO. So I would skip the tile.

Sorry remove the mirrors and if you must then tile the whole wall and get new mirrors . If you really want help take pics from further cback to show the whole wall I do not tile side walls usually but I need to see the space and also what choices you have made for tile .

What you’re proposing could be a time and money disaster. Install a pretty wallpaper.

Bathrooms need medicine cabinets, either recessed into the wall or mounted ON the wall.
You don’t necessarily need a mirror on the side wall. If you want to see the back of your hair, turn away from the mirror and use a hand-held mirror to see your hair. A mirror can be hung on a tiled wall with the correct bracket, or you can tile around a wall-hung mirror. I like wallpaper in bathrooms…whether subtle or a bit more interesting…..wallpaper made specifically for humid spaces, and installed by a professional or experienced homeowner. Be sure your bathroom has an exhaust fan to remove excess humidity. Since a bathroom sink area may be a splash zone, I always have some sort of backsplash and a side-splash for a sink counter which reaches into a corner.

Does the mirror fit tight on both sides? If not, I'd remove it, tile, and put it back while sliding it over a smidge.

I haven’t seen a home built in the last 20 years that has a medicine cabinet in it. I don’t know what that very outdated proclamation is all about. As far as the rest of your project, remove the builder-grade mirror and tile the entire wall.

Definitely remove that builder grade mirror - it will always look like a builder grade, no matter how pretty your tile is. If you do the whole wall, as Lynzy suggests, you won’t have to deal with drywall repair. Have the tiler tile around your light fixtures (if they’re in the wall) and hang a pretty framed mirror afterwards.