Determining if a power supply is isolated?
The older ones with substantial weight to them all contain transformers, so they will certainly be correctly isolated.

Most of the newer lightweight ones also contain small high-frequency transformers, so they also ought to be correctly isolated; however I would have my doubts about the very cheapest and possibly counterfeit "iphone charger" type of product.

If everybody is playing by the rules, anything with the "double-insulated" symbol (two nested square boxes) will be correctly isolated. Buy anything with this symbol from a reputable supplier and you should be good.

(For completeness : the mains isolation is usually "broken" by some small capacitors for noise suppression : these will (excepting counterfeits) be rated to high safety standards (Class Y or X2) and not considered to break the isolation for safety purposes; however there may be applications in e.g. sensitive medical electronics where even the tiny AC current they permit is too much. For all our sakes, I hope you're not asking about such applications on StackExchange! :-)