test: fix race condition in TestAPI/Delete/OK_with_container_and_subagent (#21982)

Closes https://github.com/coder/internal/issues/1345#event-22592902899

agent/agentcontainers/api_test.go

@@ -1477,14 +1477,6 @@ func TestAPI(t *testing.T) {
 					)
 				}
 
-				api := agentcontainers.NewAPI(logger, apiOpts...)
-
-				api.Start()
-				defer api.Close()
-
-				r := chi.NewRouter()
-				r.Mount("/", api.Routes())
-
 				var (
 					agentRunningCh chan struct{}
 					stopAgentCh    chan struct{}
@@ -1501,6 +1493,14 @@ func TestAPI(t *testing.T) {
 					}
 				}
 
+				api := agentcontainers.NewAPI(logger, apiOpts...)
+
+				api.Start()
+				defer api.Close()
+
+				r := chi.NewRouter()
+				r.Mount("/", api.Routes())
+
 				tickerTrap.MustWait(ctx).MustRelease(ctx)
 				tickerTrap.Close()