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There are three related changes:

1. Change ManifestUpdateManagerSystemAppBrowserTest.CheckUpdateSkipped
   to closer match how installs are done for System Web Apps i.e.
   we no longer use a manifest for the initial install.
2. Remove set_manifest() which the test used to change the manifest of
   the SWA
3. Remove a couple of other unnecessary methods now that we removed
   set_manifest().

We don't completely remove the manifest because a test still uses it.

Bug: 1158686
Change-Id: Ib9ed2f81c0b3ba877f2bc74151fc0dd9c4c1c291
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2641786
Commit-Queue: Giovanni Ortuño Urquidi <ortuno@chromium.org>
Reviewed-by: Jiewei Qian  <qjw@chromium.org>
Cr-Commit-Position: refs/heads/master@{#845970}