chore: refactor agent routines that use the v2 API (#12223)

In anticipation of needing the `LogSender` to run on a context that doesn't get immediately canceled when you `Close()` the agent, I've undertaken a little refactor to manage the goroutines that get run against the Tailnet and Agent API connection.

This handles controlling two contexts, one that gets canceled right away at the start of graceful shutdown, and another that stays up to allow graceful shutdown to complete.

coderd/coderdtest/coderdtest.go

@@ -193,7 +193,7 @@ func NewOptions(t testing.TB, options *Options) (func(http.Handler), context.Can
 		options = &Options{}
 	}
 	if options.Logger == nil {
-		logger := slogtest.Make(t, nil).Leveled(slog.LevelDebug)
+		logger := slogtest.Make(t, nil).Leveled(slog.LevelDebug).Named("coderd")
 		options.Logger = &logger
 	}
 	if options.GoogleTokenValidator == nil {