[SendTabToSelf] Adjust the show and disappear timing of omnibox icon

Pop up the icon animation shows once per window.

The icon shows when:
- highlighting the url or focus in the omnibox, and
- the user doesn't edit the url.
Once the user start typing in theomnibox or click outside the
ominbox, the icon disappears.

Also, fix the bug that "don't show omnibox icon when sync paused".

Bug: 956189, 963159
Change-Id: I556a13bf291f2d6cd0509c3c1e2c3d002b6e66dd
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1621205
Commit-Queue: Tina Wang <tinazwang@chromium.org>
Reviewed-by: Tommy Li <tommycli@chromium.org>
Reviewed-by: sebsg <sebsg@chromium.org>
Cr-Commit-Position: refs/heads/master@{#663330}
8 files changed