That's still all your infrastructure components calling out to an external service on every read --- and for what advantage?

This isn't an app server; it's an infrastructure component, running (I don't know about Tailscale here, but we use SQLite in similar uses cases) on potentially hundreds or thousands of machines.

No, you don't need to make any network call on every read with listen/notify. It will essentially be a local cache, working the same way as etcd watcher, using one postgres connection per machine.