Revert "Privatize signals in async_packet_socket.h"

This reverts commit f672636abf8b5ff5b04265986ce66d136f272d3a.

Reason for revert: Chrome wasn't quite ready.

Original change's description:
> Privatize signals in async_packet_socket.h
>
> Bug: webrtc:42222066
> Change-Id: I54e47aed3a44e4f6ebdda7ee31d6aef180da966a
> Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/424120
> Reviewed-by: Tomas Gunnarsson <tommi@webrtc.org>
> Commit-Queue: Harald Alvestrand <hta@webrtc.org>
> Cr-Commit-Position: refs/heads/main@{#46220}

Bug: webrtc:42222066
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Change-Id: Id12fcc2d30da673f5b9b51d564dbb42fccee2e7f
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/426662
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Commit-Queue: Harald Alvestrand <hta@webrtc.org>
Reviewed-by: Mirko Bonadei <mbonadei@webrtc.org>
Cr-Commit-Position: refs/heads/main@{#46223}