System Clipboard: Make all write functions commit separately.

Make write functions commit separately, so that writing of multiple types to
the system clipboard is more consistent, and so that there aren't two
parallel write implementations.

Bug: 941085
Change-Id: I056972f30f13763b9bb6b483e7ea2773a68d2fef
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1530831
Reviewed-by: Daniel Cheng <dcheng@chromium.org>
Reviewed-by: Victor Costan <pwnall@chromium.org>
Commit-Queue: Darwin Huang <huangdarwin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#643041}
11 files changed