fix: export chatd.Start to separate server lifecycle (#24761)

chatd.New() no longer auto-starts the acquire/wake loop.
Callers that want chat processing call server.Start()
explicitly. Tests that want a passive server skip Start();
heartbeat, stream janitor, and stale recovery still run.

Closes coder/internal#1502

coderd/coderd.go

@@ -794,7 +794,7 @@ func New(options *Options) *API {
 			WebpushDispatcher:              options.WebPushDispatcher,
 			UsageTracker:                   options.WorkspaceUsageTracker,
 			PrometheusRegistry:             options.PrometheusRegistry,
-		})
+		}).Start()
 		gitSyncLogger := options.Logger.Named("gitsync")
 		refresher := gitsync.NewRefresher(
 			api.resolveGitProvider,