Use the new class internally where appropriate too.
The objective is to rename it, but due to some external dependency,
it is better to copy, update dependencies and remove.
Bug: webrtc:10069
Change-Id: I8477ce5a2982933db27513cc9509f51558dafaf3
Reviewed-on: https://webrtc-review.googlesource.com/c/113265
Commit-Queue: Florent Castelli <orphis@webrtc.org>
Reviewed-by: Erik Språng <sprang@webrtc.org>
Cr-Commit-Position: refs/heads/master@{#25920}
