do you really want to save that old tile? resurfacing it (and the tub) is only good for a few years before it starts to chip and peel) The caulking between the tub and tile all needs to be scraped out and redone (don't ever grout this portion if you do get new tile. Use 100% silicone caulking for that and the vertical corners)

The person who will tile for you, he will also waterproof the tub surround after demoing all that tile?

If cost isn't the issue here, then why not just redo it? Any of these examples would look way better than painting those existing tiles.

I would recommend replacing the tile and substrate such as dura-rock board with the schluter water proofing system https://www.schluter.com/schluter-us/en_US/ to ensure you don't ever have any issues with moisture behind the wall/tile. Here are a few different looks for the subway tile that have been extremely popular

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If you have no issues with the tile other than color you may want to consider not replacing as you have a existing mud job. If done correctly it's not going anywhere and will be a pain to rip out. Then you will need to rebuild walls to plumb as the previous tile setter took care of that when floating the walls.

Creative Tile - just curious, how can you tell it’s a mud job?

in the old days they all used mud.

@btrix The use of a conventional trim tile instead of a surface trim tile. Notice how the 2x6 cap is actually curved to accommodate mud thickness. Not just flat with a rounded edge.

Thank you! I wondered if that was it! I have two bathrooms with similar tile and that cap along the sides and floor. Good to know it’s a mud job. I’m planning to leave it be in my powder room and wainscot over it.

My 1983 bath looked the same. When I ripped the tile out I discovered it was done on drywall which was moldymoldy, musky, and saturated with water..

I can't find a pic of my old tub / shower combo on my phone but my master shower was done the same way..