I'm currently talking with someone who's making a client-side mod for defining areas of the world, and I thought "cardinal components would be perfect for this"... but I can't find any info or documentation about storing things when you're connected to a server, I can only find info about how to replicate components between client and a server that also has the mod installed.

Are client-only components supported? Specifically, storing components per server world? Is this a use-case that CCA would be interested in supporting?

This is currently not supported at all, although it could indeed be interesting - I don't have the spare time to develop such a feature though, so someone else woulf have to implement clientside storage