I see no need to update the vanity and fixtures. I like the floor tiles. I would not do blue accent tiles in shower if you think you will one day replace the floor. As far as paint, I could see a pale yellow or pale blue on the gray side ( not baby blue).

I think the gray walls with a white ceiling and trim will look fine. You can reuse the mirror and have other black elements in the room ( knobs on new vanity & flooring). When we renovated our bathrooms I chose Sherwin Williams Mega Greige and it looked really nice with white sub-tiles and white wainscoting. It made the ceiling appear higher. We left the ceiling white. The tile flooring had some whites, grays and browns marbled through.

I would replace both counters and sinks. The sinks do not match so even if you do (sort of) match the brown counter they will not look like they go together.

I agree with Cpartist"s layout and like moving the closet over as suggested by D M so that bedroom 3 has easier access to the bathroom. Do you have room to have the toilet face the tub and add a linen cabinet next to the toilet? How wide is the tub toilet area?