Use GracefulExitContext for Proxy Web Endpoint service

GracefulExitContext is usually the context that should be used to be
notified of process shutdown.

ExitContext only notifies on immediate shutdowns, and gives no time to
do clean ups.

lib/service/service.go

@@ -3987,7 +3987,7 @@ func (process *TeleportProcess) initProxyEndpoint(conn *Connector) error {
 			Emitter:                   streamEmitter,
 			PluginRegistry:            process.PluginRegistry,
 			HostUUID:                  process.Config.HostUUID,
-			Context:                   process.ExitContext(),
+			Context:                   process.GracefulExitContext(),
 			StaticFS:                  fs,
 			ClusterFeatures:           process.getClusterFeatures(),
 			UI:                        cfg.Proxy.UI,