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Should this slab be moisture tested first?
Moisture coming up through a slab is the most common reason a floor coating fails. Five questions, and an honest answer about whether to test before you spend anything.
Five questions about the slab
Test before anything goes on this floor
What you have described is how a moisture problem announces itself. Vapor moving up through a slab lifts coatings and glue, and it will do the same to a new one. A calcium chloride or in-situ RH test costs a fraction of redoing a failed floor.
This is the one thing on this site we will not estimate around. Nobody can look at a photo and tell you the vapor drive.
Worth testing before you commit to a coating
Nothing here says you have a problem, but enough is unknown that a test is cheap insurance, especially for anything that seals the surface. A polish is more forgiving than a coating because it does not trap vapor the same way.
Low risk on what you have told us
An older slab, no visible signs and nothing trapped under a failed coating is the low risk picture. We would still look at it in person, because moisture is the failure we most want to catch before the work, not after.
Moisture matters less for a polish, but still check
A mechanical polish leaves the slab breathable, so vapor has somewhere to go. That makes it the more forgiving choice on a slab you are unsure about. It does not make moisture irrelevant, and it does not fix a slab that is actively wet.
Still the same rule
This works from what you tell it. Your slab gets the final say, and that needs someone standing on it. Send photos and we will price the actual job.