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In next CLs: Add more started/shutdown checks in WebAppInstallFinalizer,
WebAppInstallManager, ManifestUpdateManager.

Bug: 1084939
Change-Id: I720cbdd79998e895f5b9171e3173f89c6977be6b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2210085
Auto-Submit: Alexey Baskakov <loyso@chromium.org>
Reviewed-by: Alan Cutter <alancutter@chromium.org>
Commit-Queue: Alexey Baskakov <loyso@chromium.org>
Cr-Commit-Position: refs/heads/master@{#770931}