Private networking between organizations

Don’t think that’s possible.

However, you can carve out network-namespaces within the same org such that apps / VMs across namespaces would not be able to connect with each other over 6pn. Unfortunately, this is exactly the inverse of what you want.

Right now, I think you’d have build cross-org connectivity yourself, by either wiring up a bridge across namespaces (quite brittle and tri-icky, I’d imagine), mTLS’ing over public IPs, warping with hole-punching Tailscale tunnels, or any number of similar methods.