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.
