…nabled

Profiles were tagged as new even when the `SearchEngineChoiceTrigger`
feature was disabled.

The `"default_search_provider.choice_pending"` profile pref was wrongly
populated and needs to be deprecated. It is now replaced by
`"default_search_provider.engine_choice_pending"`.

(cherry picked from commit 745c6c6acfc47ebf887beb8dbb3fb15ff953593e)

Bug: b:330701590, b:330839066
Change-Id: I94f3e84fd7f673599d92585c4ef6ce1c25f1a574
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5380615
Commit-Queue: Nicolas Dossou-Gbété <dgn@chromium.org>
Reviewed-by: Orin Jaworski <orinj@chromium.org>
Auto-Submit: Jack Yammine <jyammine@google.com>
Reviewed-by: David Roger <droger@chromium.org>
Cr-Original-Commit-Position: refs/heads/main@{#1277839}
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5393603
Owners-Override: Krishna Govind <govind@chromium.org>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/branch-heads/6379@{#6}
Cr-Branched-From: e5b4774389ecb8a127e4fc8afbc7c2e781b67716-refs/heads/main@{#1277564}