We went with ALTCHA in the end, the open-source proof-of-work captcha suggested further up, rather than Cap. It replaced hCaptcha entirely as of #3035 (after trialling it in #2986), on fluxer.app and on self-hosted instances alike.
Challenges are issued and verified by our own API, so there's no third-party captcha service involved and no visual puzzle to solve. The browser just does a short proof-of-work in the background, which should also help with the accessibility concerns raised here.
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Comment by Hampus