There are epoxy paints for garage floors. Rustoleum is one brand. They're advertised as a DIY product but only you can decide if the work is within your skill level. If you do go with one of these products, make sure you read and follow the instructions carefully with regard to surface preparation.

I have concrete countertops but I don't wax them. One day I sprayed some Method granite cleaner on them, and found that I really like the way it cleans them and the finish that it leaves. I think that Kevin, the stone guy who told all of us about Method for dark honed granites (which I also have), said that it has conconut oil or wax or something like that in it. Maybe that's why I like the finish that it leaves, particularly after several treatments.

I doubt you are going to get helpful posts on this request. Fiberglass overlays on a concrete pool are just not very commonly done. And since you only got 10 years from the one that the prior owner installed I would offer that it's a bad idea as well. A plaster coating is much more common on a concrete pool and should last for up to 25 years if maintained properly. I am also sure you will find a ton of companies in CA who do plaster finishes. They also offer higher end pebble finishes as well that are suited for a concrete pool.

Any chance it is just layers of gray concrete paint? If you truly want to know what it is, you might use a knife you no longer like or a hatchet or other yard/garden tool you don't mind potentially nicking to whack a small piece off and take it to your local building supply store. Even if whatever it proves to be will not come off easily, I'm guessing that if any "slick" feel is removed from a veneer, a new covering might stand a better chance of adhering to it. If, however, the color is already peeling, at least try to get it all off the top lest anything you might add to it also peels off. You could outline the sides with pavers and would not need to "clean" whatever the gray is from off the sides -- avoiding that might keep from damaging your lawn/soil with chemicals -- damage can last multiple seasons. Gasoline is dangerous and even if not ignited, it can kill your grass and soak into your soil and keep anything from growing there a while. You need to be very careful trying to "clean" with it -- no wire brush ever -- no sparks anywhere near it ever. However. However. One way to see if the color/finish is paint might be to put a large spoonful of gasoline from your mower supply in the middle of the sidewalk and with a stiff plastic brush scrub a very small circle with it..