[NTP] Fix promo overlapping with toast notifications

When the delayed notification timeout was executed early, the promo was
re-shown instead of remaining hidden. Do not show the promo if the
delayed timeout was executed early.

Also adjust the notification handlers to match remote NTP
(cl/213513740). This allows us to apply float animations to the promo
as well.

Screencast: https://drive.google.com/open?id=1gnFuRL5wFO-LoqATO0t6PQx05RTmn85w

Bug: 941247
Change-Id: Ie68a3a78eb141af928c431813b8dc45fe586c800
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1518502
Commit-Queue: Kristi Park <kristipark@chromium.org>
Reviewed-by: Kyle Milka <kmilka@chromium.org>
Cr-Commit-Position: refs/heads/master@{#640590}
1 file changed