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Currently, when we switching between tabs, the intent picker icon will
disappear. This CL uses the tab helper to persist the intent picker icon
state and ensure it is up to date when switching between tabs.

BUG=801712,915949

Bug: b/120113310
Change-Id: I243773a805955b645e833719a4887905f72b311b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1605321
Commit-Queue: Maggie Cai <mxcai@chromium.org>
Reviewed-by: David Jacobo <djacobo@chromium.org>
Reviewed-by: Scott Violet <sky@chromium.org>
Reviewed-by: Alan Cutter <alancutter@chromium.org>
Cr-Commit-Position: refs/heads/master@{#660325}