There is! The API Key is literally "public". But apparently it often gets rate limited, because seemingly every Metasearch engine uses that one. I think there might also be a slightly less rate-limited one for Hacker News users if you search around (I no longer remember what it is since I got my own key in the end.)

You can get your own API key for free by emailing, but that would not be anonymous, I guess.

I don't have curl syntax to hand, but hopefully it's easy to figure out from these documents. I may come back and edit later with curl syntax if I get time:

https://about.marginalia-search.com/article/api/