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This makes some minor refactors to the usage of
AutocompleteController::in_start_.

 1. It delays setting it to false until after the UpdateResult call
    within the synchronous pass. This is more accurate, and also allows
    in_start_ to be used as a synonoym of in_synchronous_pass_.

 2. It also moves in_start_ to be an early exit condition for
    OnProviderUpdate. It likely doesn't need to be checked there at
    all, since the comments indicate it's likely ALWAYS false when
    OnProviderUpdate is called.

These refactors help pave the way for the feature to preserve the
default match during the asynchronous pass, by clarifying in the code
when the synchronous vs. asynchronous pass occurs.

Bug: 398135
Change-Id: I8f8c61b8233b1c049338dac448b6ef8f1b0e3b93
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1789823Reviewed-by: Kevin Bailey <krb@chromium.org>
Commit-Queue: Tommy Li <tommycli@chromium.org>
Cr-Commit-Position: refs/heads/master@{#694850}