Setting different custom search engines for Normal and Private Windows is unintuitive/has UI bugs

[LegalizeNukes]

Description

The video below showcases the bug that occurs when trying to set two different custom search engines for Normal and Private Windows.

I am trying to set the custom search engine "search.brave.com" for Normal Windows and a custom search engine "safe.search.brave.com" for Private Windows. There are a few UI bugs, and overall, the entire experience of setting different custom search engines for a Normal and Private Window is bit unintuitive.

custom_search_engine_bug_showcase_f.mov

Steps to reproduce

See video.

Actual result

See video.

Expected result

I should be able to select and set a custom search engine for each window type without having to switch default search engines and using the workaround as shown in the video.

Reproduces how often

Easily reproduced

Brave version (brave://version info)

Brave | 1.76.73 Chromium: 134.0.6998.45 (Official Build) (arm64)
Revision | 7ce94109896c1bebebdd37d24b4ccf28e47deef0
OS | macOS Version 15.3.1 (Build 24D70)

Channel information

• release (stable)
• beta
• nightly

Reproducibility

• with Brave Shields disabled
• with Brave Rewards disabled
• in the latest version of Chrome

Miscellaneous information

None.