If you get enough signals like that you can often narrow down a very large cohort of people to an individual.

First it's 'over 18?', then it's 'over 25?', and then 'biological sex?', 'employed?', 'enjoys posting on HN?', 'active in the early morning?' and after half a dozen questions, all with binary answers that are safe individually, you can zero in on a 23 year old woman who has a job and posts on HN in the morning.

Ask a few dozen questions like that and you'd be able to sieve an individual from a group of millions, especially if they're unlucky enough not to be absolutely typical.

Proper ZK proofs don’t work that way. N different proofs will not be linked to each other unless the circuits are written to emit a stable identifier.

Obviously if you see a bunch of proofs for known circuits coming from the same IP address then yeah, you can infer a bunch of info from that metadata.