The answer that no one likes: make it cost a nominal amount of money.

Enough to make it so bots are expensive to run.

You could just have a custom one that asks domain-specific questions (and ones which will trip up LLMs are not hard to come by.) I've seen a few forums ask such questions for registration, long before the rise of LLMs.

There are other captcha alternatives like Turnstile, for example Private Captcha, Altcha etc. - they are owned by mostly “small” independent companies, they are not visual captchas (proof-of-work based) and very accesssible.