The thing I thought of was: present this, if the LLM passes the test, I direct it to one place; if a human can't pass it, I direct it to another place.
Like, maybe this could be a way to mitigate bot traffic.
You got it backwards. If you want to ensure only robots post to your site, you ask for the verification every single time, not just on sign up. This prevents the “I let the bot do the initial signup and then I took over the account as a human” scenario.
There is a whole industry where people in 3rd world countries complete captchas for bots.