[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}
30 files changed