crash when searching via private window while having SE extension set as `Allow in private`

Description

When you have a SE extension installed and have set it as Allow in Private, searching for a term via private mode will crash the entire browser. Similar to the issue that was fixed via https://github.com/brave/brave-browser/issues/15140.

• Uploaded crash report ID: d5250000-9cfd-2306-0000-000000000000
• Uploaded crash report ID: d4250000-9cfd-2306-0000-000000000000
• Uploaded crash report ID: d3250000-9cfd-2306-0000-000000000000

Steps to Reproduce

1. download https://chrome.google.com/webstore/detail/duckduckgo-privacy-essent/bkdgflcldnnnapblkhphbgpggdiikppg/related?hl=en
2. go into brave://extensions and set DDG Privacy Essentials as Allow in private by clicking Details
3. open a private window and type in test test and click enter to start the search
4. instant crash

Actual result:

Brave instantly crashes.

Expected result:

Brave shouldn’t be crashing.

Reproduces how often:

100% reproducible using the above STR.

Brave version (brave://version info)

Brave | 1.23.69 Chromium: 90.0.4430.61 (Official Build) (64-bit)
-- | --
Revision | dced74d4124b26b14126b611853d33512b60c7b6-refs/branch-heads/4430@{#1115}
OS | Windows 10 OS Version 2009 (Build 19042.906)

Brave | 1.25.8 Chromium: 90.0.4430.61 (Official Build) nightly (64-bit)
-- | --
Revision | dced74d4124b26b14126b611853d33512b60c7b6-refs/branch-heads/4430@{#1115}
OS | Windows 10 OS Version 2009 (Build 19042.906)

Version/Channel Information:

• Can you reproduce this issue with the current release? Yes
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? N/A
• Does the issue resolve itself when disabling Brave Rewards? N/A
• Is the issue reproducible on the latest version of Chrome? N/A

Miscellaneous Information:

CCing @rebron @bsclifton @simonhong @brave/legacy_qa

[btlechowski]

Added QA/Test-All-Platforms as Tor is using different binaries for each platform

[LaurenWags]

Testing https://github.com/brave/brave-core/pull/8626 will cover the following issues:

• https://github.com/brave/brave-browser/issues/15224 (this issue)
• https://github.com/brave/brave-browser/issues/10601
• https://github.com/brave/brave-browser/issues/14218