Just bought a fixer upper with a 50 year old pool that has not been taken care of for at least 10 years. It has never been resurfaced
Looks like the pump and filter were replaced to sell the property.

The plaster is original from 50 years ago?

That's when they might have had asbestos in the plaster, so it might be possible but very unlikely.

Make sure that the chip out is done safely assuming asbestos might be in the plaster.