I’m not a paint expert, hopefully they’ll chime in, but my first thought was painting the walls the right shade of white, or a light to med gray (which I can see in the tile).

If possible, replacing hardware (faucet, knobs, towel bars) with sleek, industrial-style pieces.

Artwork, shower curtain, and a modern rug would finish it up.

ETA: I can’t find good pics of my ideas, but wanted to show these two for a general idea of mixing brown and gray:

Great Ideas Jinx. If you reface your cabinet with a dark stained finish and change the faucets, it will look cohesive. If that isn't in your budget, you might be able to paint the cabinets to hold you over until you can reface or replace the vanity.

New light paint color for the walls pulled from the tile will make a big difference.

I would price replacing the counter with a lighter, quieter prefab laminate counter. They aren't terribly expensive and might be within your budget. A six-foot version is around $100 plus install.

The color choices are limited. Greys and browns are tricky so be sure to bring a sample home to look at in your light to make sure the undertones work together.

https://www.homedepot.com/p/Hampton-Bay-8-ft-Laminate-Countertop-in-Sea-Salt-with-Tempo-Edge-and-Integrated-Backsplash-011312010819529/305470953

What colour would you suggest painting the cabinets?

A color in your counter top. If the cabinets are laminate, it could be more difficult. I don't have experience painting laminate. The darker your surfaces in the bathroom, the more light you will need. Think about adding light with different light bulbs or changing the fixture.

Brown is essentially a low intensity orange, and the complementary color to that is blue. To balance the brown that you cannot change, you could paint cabinets a light or medium blue, but not an intense blue.

Even changing the towel bar will help.

It’s not that bad really; I think if you add the right accessories it will look wonderful! I always use orange with brown - they look great together . Think about adding large vases of flowers; baskets of facial towels, vases of different colour soap bars; vivid art work and a rug- will look great!

Laminate counters like that are inexpensive to change. It has too much brown in it to work if you go in a gray direction. But a warm gray pulled from the tile will work to pull the rest together. Just that counter won’t work.

I'm with live-wire oak. You need to stay warm (blue will just make the orange even more orange!) but can go with a warm greige or pale taupe. Lightening things up will improve matters a lot.

Thanks everyone for your feedback and suggestions!!

I’m going to go with a warm off white/very light greige wall and change my hardware and vanity lighting to incorporate industrial black finishes. I can’t change the countertop for a number of reasons, unfortunately...

If you don't want to replace your mirror, you can just get a custom frame for your existing mirror. That will also help to update your bathroom. You can even get a frame that matches your hardware or your vanity.

I'm rather at a loss, because the tile is awfully like one that I'm thinking of installing in a bathroom here. As for the countertop: the least-cost way to tone down a pattern or color combination is to use more of one of the colors, so that it become the background instead of the foreground. In this case, it might work to paint the vanity (it is possible to paint laminate using a high-bonding primer, more difficult imo to paint thermofoil) one of the medium colors from the countertop.