Based on the server log, the server itself is failing to travel to the new map. Since this failed, the server is never opening a map with the ?listen option, so it won’t be able to respond to any clients that are trying to connect (this is why the client is timing out).
The “Launch” button in the editor will only cook the current level that’s open and save it in the Saved/StagedBuilds directory, which could explain the travel failure.
One more thing to try is using the Package Project option. This will cook all the levels in your project, and should allow the server to travel to any of them.