The injected client.js will try to reconnect to the sse endpoint as soon as the port is bound

[evanweible-wf]

1. Run webdev_proxy serve
2. Open the served port in a chrome browser tab
3. Terminate the webdev_proxy serve instance
4. Restart webdev_proxy serve and note that the browser tab immediately tries to reestablish its SSE connection which produces an error in the server logs because the underlying webdev serve process has not yet started

We likely just need to detect this scenario during startup and silence the error on first request to that endpoint (it ends up succeeding as soon as webdev serve has started up).