I'm not sure that the style of the vanity doors is in keeping with the feel of the tile or fixtures. What you have existing speaks traditional to me. Perhaps you can replace the doors. I love the mirrors. How do you feel about a dark counter top? I think you have good bones to start your update with. Good luck!

Do you prefer light or dark cupboards? I love the taupe,but the color of the cabinet doesn't work with it. Here's a picture with a taupe counter top and dark cupboards. You could go white or dark, and paint the wall a pale, soft green. Green and taupe is lovely together.
https://www.houzz.com/photos/320-sycamore-traditional-bathroom-phvw-vp~34089

Keep the wood cabinet and update with a new granite countertop and new lighting. And paint the tiles! Yes, there is a paint out there that works amazing on tile and then you can rid yourself of the pinky tones and mismatched tiles in the shower. I would paint it all white. You can keep the floors. Then I would change the cabinet pulls to shiny nickel. Behind the sinks you can run the granite up the wall about 6 - 12". Keep the mirrors and faucets and change the light fixtures. I would see if you can put one over each mirror instead of two and then have a double light. This will look much nicer and I would use the same nickel metal on the lights as on the pulls. Once this is all done you'll be able to add your favourite colour! You can add teal or hot pink or navy... or mix it up for the season. A white floor mat will help lighten the floor and connect it to the newly painted tiles. As for granite colour... choose something that has a fleck of the floor colour, is very veiny (to add texture), and has some browns and whites in it too. Keep the sinks white and you can have them undermounted.
Keep us all posted!

I like the the ideas of painting the cabinets like in the 320 Sycamore photo that qoais posted. All of your fixtures are bronze so changing them all out would be expensive. With the bronze fixtures, black paint might be a little too dark. Check into lighter paint colors for the cabinets. I don't think your bathroom needs a lot of updating. It looks nice now!

What is the name of the paint that you can put on tiles, Toronto? That sounds very intriguing!

Keep the vanity. Buy new doors. Paint the entire vanity and the walls.
New countertop. If you go with a stone, then do undermount sinks.
New Mirrors.

That would be the minimum I would do, unless you want to change out all the ORB to a matte pewter. But really, you could reuse all the accessories and fixtures for another few years.

Oh, and try buying several different light bulbs (halogen/LED/cool/warm) and try each one of them in there - you might find a color that will mitigate the pinky-taupe tile.

Congrats on your first post - wish you the best of luck with your bathroom updates!