I work on nginx cache modules for a CDN provider.
While websockets can be proxied, they’re impractical to cache. There are no turn key solutions for this that I’m aware of, but an interesting approach might be to build something on top of NChan with some custom logic in ngx_lua.
I agree with you that web proxy cache’s aren’t the silver bullet solution. They need to be part of a more holistic approach, which should start with optimizing the database queries.
Caching with auth is possible, but it’s a whole can of worms that should be a last resort, not a first one.
Caddy is great, I’ve been using it for all greenfield projects.
P. S. Have you checked out the Caddy API?