Subdomain does not resolve
The path-routed front door works, but the host-routed subdomain URL fails to resolve.
Symptom
The front-door URL works, but <slug>.<base-domain>:9000 does not resolve in the browser or in a client.
Cause
The configured base domain does not have wildcard resolution, the browser does not special-case that domain, or the request is being made with a suffix the proxy does not accept. supa.localhost resolves in Chromium and Firefox but not in Safari; lvh.me is a public wildcard and must be opted into as an extra suffix.
Fix
Use the front door instead
The path-routed URL does not depend on DNS and is the simpler default for local clients.
Check the effective base domain
Admin Settings shows whether the value comes from the database, the environment or the default.
Choose a resolvable domain
Use a base domain with wildcard resolution for the browser you are testing in.
Opt in deliberately if needed
Accepting lvh.me widens host routing; enable it only if you understand the trade-off.
Prevention
Prefer the front door in client configuration. Keep the subdomain proxy for the cases where host routing is genuinely useful.
Another thing to check
If the host resolves but the request is denied, the problem is access rather than DNS. Check that your manager session owns the project and that the link or slug matches the project you intended.