I would just stay neutral. My immediate thought is white vanity with a white quartz top that has some veining in it. (Boring?)
But you may be able to find a granite that compliments the flooring color nicely. Since it’s a natural stone you’d have to go look at a granite yard. But you can often find good deals for vanity tops.

If you like green, there is a granite called Costa rose that has a light sea green with white and rose in it. It’s pretty popular in my area.

White on white or a combination of white, black, & grey. Stay neutral & match rug/mat & towels to cabinet & counter top. New faucets will be a huge update.
Take samples of wall color, linens, cabinet, counter, & photo of the floor to pick out accessories & Art. Bring the slightest bit of white washed mauve into your art & decor so it ties in but doesn't dominate. The floor will be less noticeable when the other elements are updated. Try wispy or impressionist for the decor. Think Monet.

Wait on the whole thing until you can do the floor. It's a total waste of time , money , and effort. Porcelain tile is inexpensive. Simply save some more money. Right now........it is a plan to put lipstick on a pig. You will still have a pig : )

if budget is tight and you would like to feel better about your room now - have you considered changing the counter top to match/blend with the doors and change hardware (basins and taps)? you could add some individuality with your accessories - wood tray for soaps and lotions to bring in the wood from the doors? i agree lightening and brightening will help the floor recede. i think it is the color of the counter top which is having the greatest impact in making the scheme seem dated. The cabinet style, i think, is quite modernist/scandi as it is floating.

or gives the appearance of doing so.

Tile is cheap. Is it the labor you cannot afford? Because I would save up and wait to change it all. NOTHING is going to look good with pink tile.

Wait until you can do the floor.

I agree why throw money at a floor that you hate .but really if you change the vanity now you will have to find one that is exactly like the one you have size wise since chances are the tile does not go under the vanity. Bathrooms are almost always gut jobs to be done right so wait until you can do the whole thing.

Another vote for waiting until you can complete the project including a new floor.

I am in a similar situation in trying to update a mauve bathroom without spending too much. That said, that is a large vanity and I assume it would be pricey to replace....so I would not invest that money and leave the old mauve floor. Either I would wait and just replace it all at once or do some cheaper updates with paint. You could paint out the vanity. There are a lot of tutorials/ideas about what to do with that type of would trim cabinet. Also I've seen some things like this http://adaesthetic.com/spray-painted-bathroom-counter/ about painting/refinishing a laminate counter. I also saw where some people covered their bathroom counter (and sink) in a thin layer of concrete! Good luck :)