Lots of old pools have stains.

Whether they are a "problem" depends on you. Stains don't interfere with swimmers or pool water.

But will it get worse? Probably. Can you fix it by re-plastering? Maybe. Ask your plastering contractor. Local skills vary a lot, and it would be useless for me to speculate on methods that aren't available to you locally.

Could you fix it yourself? Dunno. I could fix it, myself, even though I've never been a pool contractor or a plastering contractor. But I do have 20+ years of varied construction and repair experience.

What I would do (probably! I haven't seen it) is
  • Drain the pool
  • Keep the pool surface wet with a sprinkler, connected to a pump in the deep area
  • Chip out the gunite to expose the rebar.
  • Refill with a high-strength patching cement (like this)
  • Finish with plaster (white cement / marble dust)
  • Refill.
But, that can't be done in super-hot OR super-cold weather without risking damage to your pool