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Moves callbacks run on receiving ResponseMessage to a new class. This
will be useful for p2p connection changes. Upcoming patch will move logic
from SharingService to SharingFCMSender, so now PeerConnectionManager
(in the future) can avoid dependency on SharingService for
signalling messages.

Bug: 1018274
Change-Id: I39ebfe0ef1862b6caa8a0c387e92ff0da797b1ca
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1882320Reviewed-by: Richard Knoll <knollr@chromium.org>
Commit-Queue: Himanshu Jaju <himanshujaju@chromium.org>
Cr-Commit-Position: refs/heads/master@{#710715}