https://nj.gov/labor/myleavebenefits/help/faq/fli.shtml

NJ FLI link above. Note that FLI and FMLA/NJFLA are different programs but often run concurrently. FLI is wage replacement, the others provide for protected leave for qualified employees. I'm not an expert but I did use FLI for bonding time in 2020 when the program was a 6 week max with a weekly benefit max of $881. It's now 12 weeks and 85% of salary up to $1025/wk for 2023 (must make $1206/wk+ to maximize).

All that being said, I don't think there's any advantage to working part-time while on FLI unless you job isn't protected, and it's some sort of deal with your employer to keep your job. The state FAQ doesn't address it.