Reland "[Video Capture] Switch usage in Chromium Browser process to the new multi-client API"

This is a reland of 86e7aa883c95d551a450f71dc346fca4e31ea672

Revert was due to flaky test failures on MacOS 10.12.
The flakiness already existed before this CL.
The flaky test has been disabled.
https://chromium-review.googlesource.com/c/chromium/src/+/1501213

This reland is identical to the original attempt.

TBR=emircan@chromium.org, meacer@chromium.org

Original change's description:
> [Video Capture] Switch usage in Chromium Browser process to the new multi-client API
>
> The video capture service offers a new API for opening capture devices
> in a way that allows them to be shared by multiple clients. This CL
> switches one such client, i.e. the Chromium Browser process, over to
> that new API. This enables other clients to share access to capture
> devices with the Chromium Browser process.
>
> Design Doc: https://docs.google.com/document/d/1mYnsZfLBRmbsDpUtfb6C7dzhfw2Kcxg_-uiG_6MnWVQ/edit?usp=sharing
>
> Test: content_browsertests --gtest_filter=WebRtcVideoCaptureSharedDeviceBrowserTest.*
> Bug: 783442
> Change-Id: I9c236f03e315cdafdc07429f3213fa4d11b43b34
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1399454
> Commit-Queue: Christian Fremerey <chfremer@chromium.org>
> Reviewed-by: Mustafa Emre Acer <meacer@chromium.org>
> Reviewed-by: Emircan Uysaler <emircan@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#637405}

Bug: 783442
Change-Id: I7dca38334bc78e400daa311fa0444173add9548d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1504230
Commit-Queue: Christian Fremerey <chfremer@chromium.org>
Reviewed-by: Mustafa Emre Acer <meacer@chromium.org>
Reviewed-by: Christian Fremerey <chfremer@chromium.org>
Cr-Commit-Position: refs/heads/master@{#637873}
30 files changed