Remove usage of rtc::MessageHandler in peer_connection example

Bug: webrtc:9702
Change-Id: I2d688461858d9b6f06a0f7928f3cff7c6a7b7db9
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/272080
Auto-Submit: Danil Chapovalov <danilchap@webrtc.org>
Reviewed-by: Tomas Gunnarsson <tommi@webrtc.org>
Commit-Queue: Danil Chapovalov <danilchap@webrtc.org>
Cr-Commit-Position: refs/heads/main@{#37813}
diff --git a/examples/BUILD.gn b/examples/BUILD.gn
index 17cfc7b3..e683c19 100644
--- a/examples/BUILD.gn
+++ b/examples/BUILD.gn
@@ -693,6 +693,8 @@
       "../api:scoped_refptr",
       "../api/audio:audio_mixer_api",
       "../api/audio_codecs:audio_codecs_api",
+      "../api/task_queue:pending_task_safety_flag",
+      "../api/units:time_delta",
       "../api/video:video_frame",
       "../api/video:video_rtp_headers",
       "../api/video_codecs:video_codecs_api",