I am not sure of the current regs in NY or NJ, but here in California and unlicensed “handyman” can do repair work if the cost of such work is below a certain threshold dollar amount. I can’t recall what that amount is, but I think it is around $250-500. The California Department of Consumer Affairs is the relevant authority on this. Local jurisdictions (mainly cities like San Francisco and LA) have further restrictions and take precedence.
One thing you cannot do is modify or install new waste and supply pipes, run new electrical circuits, etc. these require a licensed tradesman or may, in some locales, be done by homeowners with an approved permit and inspection. Replacing a worn faucet gasket or internal toilet workings is probably OK…
NtP