Huh, I run these forums with Caddy and don’t see those errors. (I do see lots of EOF errors but I think that’s okay.) Are you sure your Discourse is set up right?
I proxied Discourse containers for a while, too, I even did some work to get it running out of a subfolder rather than a subdomain (long polling became an issue there though). I had Caddy proxy to it via Linux socket.
No such site at :80 is either a misconfiguration of Caddyfile (bad vhost?) or simply someone having a domain pointed at your server that Caddy isn’t configured to serve.