Social security is taxable in most cases. The rules are complicated, but if your total combined income is above a certain amount, your social security payments are taxable.
The reason this is not double taxation is that there is no direct correlation between the taxes you pay and the benefits you get. When you pay Social Security tax, it is not going into an account with your name on it. Instead, it is used to pay for the benefits of the current retirees. When you retire, your benefits are paid out of the money they are collecting from the current workers.
Paid Family Leave is a New York state-specific benefit. It is not directly paid for by the state government, however. Instead, the state has mandated that employers offer the insurance to the employees, regulated the benefits, standardized pricing, and required participation. But it is private insurance carriers that actually manage the program.
Because it is going through private insurance, the premiums you pay are not technically taxes, and the benefits you get are not technically government payments.
From what I can tell, both the premiums that you pay and the benefits that you receive are taxable. There are details about this in Notice N-17-12 from the New York State Department of Taxation and Finance.
There does seem to be a bit of a double-standard here, because with disability insurance (which Paid Family Leave resembles) if you pay the insurance premiums with after tax dollars, you generally don't pay tax on the benefits. Unfortunately, it seems that Paid Family Leave benefits are paid for with after-tax dollars AND any benefits you receive are also taxable. I'm not sure what the justification for that is, but tax law doesn't have to make sense.