So, it would probably take a lot of acid to get to a uniform finish and that would make it super rough.I took a sharp wood chisel and scraped a small spot to see if the stains are just on the surface or if they are deep, and I definitely had to scrape up a little plaster to remove stain.
You can diamond polish it, but that can be expensive and not everyone can do diamond polishing.
I would probably fill it and get it back to functional while you explore the options for what can be done next.
You now have a much better idea about what you're dealing with.
The current company seems somewhat unreliable, so maybe get some estimates from other companies to see what they recommend and prices.
The pool should be safe and usable and the discoloration is mostly cosmetic.