How about stucco to smooth it out and provide an even color. It would also be quite thin.

Keep it as is. It's really cool.

Didn't I just see a house reno - I'm thinking it was European - featured on Houzz where they found pink plaster/stone walls in the kitchen and were thrilled. They left them. Darn. Now I can't find the story but it wasn't too long ago.

If you really need to cover it, look at a product called American Clay. It's a natural earth plaster that's easy to work with and also thin. I applied it myself on almost every wall in our farmhouse.

Apply whatever waterproofing system you are using, then skim coat and paint with a really tough light colored paint that as resistant to scrapes and dings as you can get. It looks like the pink stuff was applied over the rocks. It'd probably be a good idea to test for lead paint yet again on this spot.

Scrape and clean the surface real good using a metal brush or if you can rent a surface grinder that's even better. After you done vacuum the surface and apply a few coats of good masonry bonding primer and after that you can apply any masonry finish out there, it will make that staircase look as it was built yesterday, it's inexpensive to do that just the prep work a little time consuming.

The pink is great, but that exposed Romex has got to be covered. Maybe fish it through your new wall.