Here is natural choice with the same tile

If you paint the walls a soft off white, you may not need to replace the countertop and paint the cabinet, they'll look fine. The gray is very dreary.

Below are walls in BM Natural Cream, white vanity and mirror frame, brass hardware and faucet.

Natural Choice does look better with the floor tile, but if you painted the bathroom that color you might end up with something uninteresting. I would be looking for a blue or green. Or whatever that gray is, but lighter. I do think the countertop and faucets need to be changed to complete the update. Can't see the light fixture(s) over the sink very well, but if they're also original, they are due for a change as well. The boob light over the toilet should be changed as well. Look for something semi-flush that is more decorative.

I think the room needs more colour. I'd consider the walls in a light green and paint the vanity a darker green.

A new marble or quartz counter, new faucets and light fixtures and new hardware on the vanity.

Or bright white walls would look very nice with a dark green vanity.

I love this dark green vanity colour. I'd pair bright white towels and bring in some wood tones as well, maybe some shelves or art for the walls with wooden frames.

This room is lovely. A warm white tile with sage green on the vanity. These choices would work well in your bath.

Note the double round mirrors. You could replace your large mirror with something like these.

This one shows a nice mid green vanity together with a creamy beige colour scheme which might work well with your floor tile. I love the depth of the counter top on this vanity - adds a little bit more luxe to the look and yes to the brass fixtures and handles on the vanity.

Soft cream is great in here.

I am a little confused by your fear that the grout will look dirty.

Grout is chosen to minimize the look of the lines between the tiles. You wouldn't want bright white grout. You have the tile next to the Pure White trim and the toilet and it is fine.

I can't tell what color gray you have painted, especially with the yellow toned lights. It looks much more blue gray toward the toilet and more green gray toward the sink. I believe it is due to lighting.

Did you have just this one room painted or the whole home? Is this off of a hallway or off the master?

What is the color scheme of the home? Is everything gray and white? Is the flooring just in the bathroom or throughout the home?

You want rooms to coordinate, but not necessarily match. Often the bathrooms get more color than the rooms because there isn't much opportunity to add color without using color on the walls. Your living room can have colors in the upholstery or area rug or art or accessories. Bedrooms can have color in the bedding, area rug. art and decor.

Bathrooms can bring in those colors either through wall color, wall paper or a colored vanity and coordinated with your towels.

I would update the lighting - getting whiter lights and getting new fixtures. Especially the boob lite on the ceiling.

Why did you choose different neutrals for different rooms? It isn't necessarily bad to have different colors, but I am not sure what the overall vision is or how things are flowing from room to room.

Here are some examples of whole home color pallets and how they can work. It isn't just wall color, it is a combination of flooring, wall color, art, decor and furnishings that pull everything together into a cohesive space.

This one goes from green to purple and green to purple to transition from one color to the next.

This one uses the teal and touches of gold from space to space. . .

This home uses the black accents in every room along with colors from the living room throughout the home.

This home again uses the colors in the main living space to tie the rest of the home together

I love the bold use of color in this home with everything coordinating with the backsplash in the kitchen

Here we show the same bold colors from the front entry throughout the home

This one uses very little color, but you notice the warm gold tones and plants that pull things together . . . I love that they brought the black flooring from the kitchen into the dining room area rug. . .

Two simple suggestions to take focus off the floor before you do any more substantial changes:

--Indoor outdoor runner

Safavieh Jasper 100 Collection JSP114 Rug, Grey/Gold, 2'x10' · More Info

--Art on the wall seen as you enter--this palette of pale grays, blues, ivory, and feeling

Blue Polystone Coastal Beach Framed Wall Art 40" x 2" x 40" · More Info

--pale blue shower curtain to echo whatever rug and art work you get.

--If you keep items on the vanity top, choose natural baskets.