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This change converts document-scoped FileSystemManager client in
blink to use BrowserInterfaceBrokerProxy as a use case of a callback
dispatched on the IO thread.

Bug: 936482
Change-Id: I3afba1264396bb9b916efb75c6594797ad581407
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1709723
Commit-Queue: Oksana Zhuravlova <oksamyt@chromium.org>
Reviewed-by: Alex Moshchuk <alexmos@chromium.org>
Reviewed-by: Tom Sepez <tsepez@chromium.org>
Reviewed-by: Marijn Kruisselbrink <mek@chromium.org>
Reviewed-by: Ken Rockot <rockot@google.com>
Cr-Commit-Position: refs/heads/master@{#685378}