Probably roughly nothing.
I pulled my (small) suburban cities budget which is a many hundred page long PDF and parks and rec runs 40-something neighborhood city playground type parks and 2 pools on 2.3 million total per year. Of which staggeringly only 1.5 mil are wages (we live in a rough climate, maintenance costs are high, over $100K spend on electric bills alone, etc).
On the revenue side the two public pools combined pulled in about 1/3 of a million from fees collected at the door. Its pretty cheap compared to commercial entertainment (movie, restaurant, etc), they could certainly charge more without excluding too many people, given how much it costs to live here.
I know from experience that they have a couple kid lifeguards at each pool all the time so lets say 10 total staff at all instants (LOL no) at $15/hr for 10 or so hours per day (LOL no not open that much), open about 100 days a year (LOL no they'd be ice skating in the spring on the pool if that were the case), if I multiplied this out correctly in my head, at $15/hr, the kid lifeguards cost $150K/yr while bringing in $340K of revenue. Note that I don't have the misfortune of living in CA, so the actual cost of a seasons lifeguards at the two pools is more like $80K.
The cities very gross profit margin if by a miracle pools were free to build and maintain, just revenue divided by kid labor, is roughly $340K/$80K right now and if the min wage were $15 it would "collapse" to $340K/$150K which still ain't bad.
Honestly I suspect the pool spends more on chlorine and electricity than on the kids labor.
The capital cost is no laughing matter. The most recent ADA compliant complete remodel was something like $2M which for that one pool is roughly a decades revenue.
This quick analysis leads to the conclusion that open hours for the pool are insanely profitable, and the "pool biz" is overall dominated by capital costs. The kids pay is irrelevant.