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This CL updates Nearby Share's NearbyProcessManager class to use the
newly-created chrome::nearby::NearbyProcessManager internally in order
to make connections to the Nearby utility process.

In the long-term, Nearby Share's version should be renamed or
potentially removed altogether, but this is not within the scope of the
bug fix, so I've added a TODO to take care of this.

Bug: 1130069
Change-Id: I0f8eb7e29e83ffbc6ce428eeaacd151a294d5ef1
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2459572
Commit-Queue: Kyle Horimoto <khorimoto@chromium.org>
Reviewed-by: James Vecore <vecore@google.com>
Cr-Commit-Position: refs/heads/master@{#817688}