I agree, it's a core piece of infra and has to be self-hostable. I launched this site just to get the idea out there for people to play around with, but can definitely ship self-hosting this weekend.
Self-hostable is actually in development right now, but I'm struggling with deciding the path forward:
1) PKCE for OAuth so connai.dev owns the oauth client setup for each app
2) Another connection mechanism for each of these apps like storing creds
For now I've just moved to having the self hosting user own the OAuth setup too, but that's a terrible setup experience.