Yaha I have done this before. My suggestion is to first find out what surfaces you’re dealing with because all services need a special preparation if you’re going to paint them.
There are many techniques to painting and finishes like chalk paint, and more shiny finish like satin or gloss to wipe easier in a bathroom.
Decode the finish you want and go from
So you could paint it and replace the top? If it needs it and if that's in the budget? If not, just painting the base and replacing the hardware can make a huge difference!!
How can I paint my metal green bathtub and stay for a long time?