ApiClient.buildDio takes on401; the library's dioProvider wires it to
the auth controller's clearSession. The router redirect already handles
navigation away from authed screens once the session goes null.
HomeScreen surfaces the banner on connection_refused with Retry +
Change URL.
Cold launch flow: no server-url -> /server-url. URL set, no token ->
/login. Token present -> /home with shell. VersionGate runs once when
the URL changes, hits /healthz, blocks if min_client_version > package
version. /home is a placeholder until Task 14.
Replaces Navigator.pushReplacementNamed in server_url_screen +
login_screen with context.go now that go_router owns the routes.
bvandeusen