You could get one big mirror and install sconces on top. Like this: https://www.houzz.com/photos/kara-weik-©-2012-houzz-traditional-bathroom-dallas-phvw-vp~1588585 But then you would lose the pretty mirrors. Is the middle sconce centered between the sinks?

Here is your dilemma. if you take down those fixtures there will be two holes in the mirror, that being said, they will be up high and most likely off center. So, to get new lighting that is not stuck in the corners, and covers the holes behind it, might be next to impossible unless you run a thick bar that covers the space. But some times back in the day they only drug wire over and did not put in actual junction boxes, so the bringing it to code might be another issue. 1. take one of the lights down and see what is going on 2. probably have to replace the mirror and move the electrical location.

The junction box for the light is probably mounted to a stud, which doesn't happen to be centered on the vanity. There are ways of adjusting the box's position, or replacing it with an old work box that can be cut into the drywall just about anywhere. However, in many cases, moving that box wouldn't be trivial. At the very least it would require drywall patching, and there's a good chance the electrician would have to fish a new cable to the box because the existing one wouldn't be long enough. It;s up to you, but if it were my house, I probably wouldn't bother.

This is a shared wall with another bathroom that has a recessed medicine cabinet that is 24” wide (in the exact spot where my mirror needs to be). Recessed of course fits between studs. And the framing in the wall may have been altered for it to fit. What you need to know is the stud distance center to center. Or the exact size of the cavity between the studs. Because what is billed as a 24" medicine cabinet may be sized to fit in the recess between 24" OC framing. The actual space between the studs would be approximately 22.5" If that is the case, then a 24" surface mount medicine cabinet would work. Signature Hardware Trossman 24" x 36" Framed 1 Door Medicine Cabinet But they lucked out with getting a recessed medicine cabinet! Yes, they did. But you can have a surface mount medicine cabinet which would be very much in tune with your old house. Two of my vintage ones: If all else failed, I would make a custom vintage style one. Would need to keep in mind how far the sconces project light from the wall & possibly add mounting blocks behind them to get them farther away from the wall.