It's still considered safe to call AES-GCM with a single key and a randomly generated nonce 2^32 times [1], most practical systems don't come anywhere near this limit. And there's AES-GCM-SIV that solves nonce reuse (mostly), though it's not available in the Web Cryptography API at the moment.
I don't personally care, and probably wouldn't even sev:info a random GCM nonce in an assessment, but I would also choose extended-nonce Chapoly in preference to GCM in part because of this issue.
1: https://csrc.nist.gov/csrc/media/Projects/crypto-publication...