I would take the lightest color from your shower tile and use that for your cabinet color.

You can't really put gray floor tile without changing out the shower tile too. I would paint the cabinets an off white, and maybe remove the decorative tile in the shower and putting in something a little less busy. Get rid of the yellow paint too.

Additionally, removing the old floor tile rather than laying new tile over the old tile is considered a better practice. Additionally, gray is considered a fading trend in many areas. If you love it, great. If you are just concerned about things feeling dated, then you may want to think carefully about how you want to proceed.

Paint the cabinets and use the same color on the mirror frame. That and new wall paint may get you 90% of the way to where you need to go! I surely wouldn't mess with anything in the shower, or you'll wreck the waterproofing.