Fixed crash when searching from omnibox in tor window with search engine extension (uplift to 1.23.x)

[simonhong]

Uplift of #8460
Resolves brave/brave-browser#15140

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• You have tested your change on Nightly.
• This contains text which needs to be translated.
  • There are more than 7 days before the release.
  • I've notified folks in #l10n on Slack that translations are needed.
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Post-merge checklist:

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[kjozwiak]

test-browser failed on macOS as per https://ci.brave.com/job/pr-brave-browser-pr8460_search_engine_extension_issues_1.23.x-macos/1/execution/node/242/log/ & https://ci.brave.com/job/pr-brave-browser-pr8460_search_engine_extension_issues_1.23.x-macos/1/execution/node/245/log/. However, these failures are known and unrelated to this specific PR.

22:09:57  6 tests crashed:
22:09:57      BraveAdsBrowserTest/BraveAdsUpgradeBrowserTest.UpgradePath/PreferencesForVersion062WithRewardsEnabled_ForSupportedLocale_ForUnsupportedLocale_RewardsShouldBeEnabled_AdsShouldBeDisabled (../../brave/components/brave_ads/browser/ads_service_browsertest.cc:1004)
22:09:57      BraveStatsUpdaterBrowserTest.StatsUpdaterMigration (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:275)
22:09:57      BraveStatsUpdaterBrowserTest.StatsUpdaterSetsFirstCheckPreference (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:154)
22:09:57      BraveStatsUpdaterBrowserTest.StatsUpdaterStartupPingWithDefaultReferralCode (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:229)
22:09:57      BraveStatsUpdaterBrowserTest.StatsUpdaterStartupPingWithReferralCode (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:327)
22:09:57      BraveStatsUpdaterBrowserTest.StatsUpdaterThresholdSetsFirstCheckPreference (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:191)

test-browser failed on Linux as per https://ci.brave.com/job/pr-brave-browser-pr8460_search_engine_extension_issues_1.23.x-linux/2/execution/node/242/log/ & https://ci.brave.com/job/pr-brave-browser-pr8460_search_engine_extension_issues_1.23.x-linux/2/execution/node/245/log/. However, these failures are known and unrelated to this specific PR.

23:41:54  5 tests crashed:
23:41:54      BraveStatsUpdaterBrowserTest.StatsUpdaterMigration (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:275)
23:41:54      BraveStatsUpdaterBrowserTest.StatsUpdaterSetsFirstCheckPreference (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:154)
23:41:54      BraveStatsUpdaterBrowserTest.StatsUpdaterStartupPingWithDefaultReferralCode (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:229)
23:41:54      BraveStatsUpdaterBrowserTest.StatsUpdaterStartupPingWithReferralCode (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:327)
23:41:54      BraveStatsUpdaterBrowserTest.StatsUpdaterThresholdSetsFirstCheckPreference (../../brave/browser/brave_stats/brave_stats_updater_browsertest.cc:191)

[kjozwiak]

Uplift into 1.23.x approved after deliberating with @brave/uplift-approvers. QA has verified the PR on Nightly as per #8460 (comment). However, we'll still need to get brave/brave-browser#15224 addressed.