"Deploy succeeded but unreachable" is almost always one of these (docs):

No public domain generated — a service doesn't get a URL automatically. Service → Settings → Networking → Generate Domain.

App listening on the wrong host/port. Your server must bind to 0.0.0.0 (not localhost/127.0.0.1) and listen on the PORT env var Railway injects. E.g. Node: app.listen(process.env.PORT || 3000, "0.0.0.0").

Target port mismatch — if the domain's target port doesn't match the port your app listens on, you get 502 "Application failed to respond." Edit the domain in Settings → Networking and pick the right port.

If you can share what the URL returns (502? 404? timeout?) and a snippet of your deploy logs showing the "listening on ..." line, it's easy to pin down which one this is.