Ensure the proxy service shuts down properly in case of partial init

[hugoShaka]

While fixing a flaky test in #50702 I observed that bothprocess.Close() and process.Shutdown() were hanging.

Down the rabbit hole was the initProxyEndpoint doing an incomplete startup and not cleaning up the services it started.

This PR ensures that proxy.shutdown is registered before we start running the proxy.* components so we have a chance to cleanup even if something goes wrong and we never finish the init.

Explanation:

In the PR I linked, I tried to wait for shutdown before cleaning up channels created by the test. This failed because initProxyEndpoint:

• creates the proxy.web service without process.ExitContext() (http.Server doesn't take any context)
• tries to create many components including db:proxy
• those component use authClient to retrieve information and can fail to get created
• finally registers the OnExit() function closing the proxy.web server and causing the proxy.web service to exit.

Now if anything else bad happens between the proxy:web registration and the proxy.shutdown registration (e.g. we do a shutdown and close the auth client), the proxy.web service will continue to run and block the shutdown. This also leaves dangling routines and resources. This is an issue in tests as we quickly start/stop teleport instances.