fix(agent): start rpty lifecycle after all reads/writes (#15535)

Fixes https://github.com/coder/internal/issues/214

#15475 missed that we also write to `rpty` after starting
`rpty.lifecycle()`.
This PR moves the function call right at the end. Hopefully this should
address the data races before we go resorting to mutexes.

agent/reconnectingpty/screen.go

@@ -78,8 +78,6 @@ func newScreen(ctx context.Context, cmd *pty.Cmd, options *Options, logger slog.
 	}
 	rpty.id = hex.EncodeToString(buf)
 
-	go rpty.lifecycle(ctx, logger)
-
 	settings := []string{
 		// Disable the startup message that appears for five seconds.
 		"startup_message off",
@@ -124,6 +122,8 @@ func newScreen(ctx context.Context, cmd *pty.Cmd, options *Options, logger slog.
 		return rpty
 	}
 
+	go rpty.lifecycle(ctx, logger)
+
 	return rpty
 }