Not seeing what the off balance is other than that window, which is quite odd. Why exactly are you looking to change the cabinets?

They’re beat. Over 30 years old.

First, can we see more pix of the entire room? Is this an older home? If yes, I’d try to maintain the vintage feel. I would re-think the vessel sinks - do a search here. They aren’t very popular for several reasons. If this was my bathroom, I’d keep the vanity and paint it one color. I’d install taller mirrors and remove center mirror, change lights. I’d use marble for tops and chrome or polished nickel fixtures for a classic look.

I would nix the vessel sinks. they are cool looking but messy as heck: water all over the place. You can get beautiful sinks online. i once had one that was a sea shell.

I'm not sure what the OP feels is off balance. A lot of it is balanced. The outlets aren't, and the personal mirror on one side vs towel bar isn't. To me the lights are pretty huge and stick out a lot, so maybe that's it. The combo of those with the windows and three mirror wall action is a bit much for me too. The cabinetry might be old, but it looks almost perfectly symmetrical to me.

I see the off balance in the amount of space on either side of the window. The sink on the right is not lined up with the center of the mirror.

I think your idea works. You could also do a shallow linen cabinet on the right side of the cabinetry.

Be sure to allow for a filler near the doorway and can you do the standard 21 inch deep vanity?

I would do a custom countertop with undermount sink.