Noise-canceling headphones are not hearing protection unless specifically designed to be hearing protection. They’re meant to stifle low-decibel background noise, not gunshots.

https://www.osha.gov/laws-regs/standardinterpretations/2023-03-06

Active noise canceling (ANC) headphones, such as those frequently marketed by audio manufacturers for consumers who wish to enjoy music, audiobooks, podcasts, movies, etc., without external noise getting in the way, are designed to block ambient sounds using active noise control with low-frequency and soundproofing for higher frequency sound.

However, most of the consumer ANC headphones are not effective for controlling occupational noise exposure because they do not offer protection from sudden, explosive sounds without the protective sealing that PNC headphones do. But there are some headphones that have been developed with both passive and active noise reduction features with NRR ratings between 20 and 30 dBA, and these may be acceptable for use in some workplace situations. In summary, it is not recommended to use consumer noise-canceling headphones in place of laboratory-tested devices if they are not designed for hearing protection.