`Yahoo! JAPAN` not being placed in first position via `Normal` & `Private` SE after upgrade

[kjozwiak]

Description

As per the spec via https://github.com/brave/internal/issues/1227, Yahoo! JAPAN is not being added into the first position via the following:

• Desktop --> being added last in both brave://settings/search/defaultSearch
• Desktop --> being added last in both brave://settings/search/privateSearch
• Android --> being added last under Standard Tab

However, looks like Yahoo! JAPAN is being added in the correct position on Android via Private Tab

Steps to reproduce

Perquisites: ensure that your language/country and region are set as Japan

Desktop

1. install 1.78.44 Chromium: 134.0.6998.95 (build without the Japan PR)
2. upgrade to 1.78.58 Chromium: 135.0.7049.26 (build with Japan Phase 1 PR but without Phase 2 PR)
3. notice Yahoo! JAPAN is at the bottom of brave://settings/search/defaultSearch
4. notice Yahoo| JAPAN is at the bottom of brave://settings/search/privateSearch

They should be at the top/first position rather than at the bottom of the SE list.

Android

1. install 1.78.44 Chromium: 134.0.6998.95 (build without the Japan PR)
2. upgrade to 1.78.58 Chromium: 135.0.7049.26 (build with Japan Phase 1 PR but without Phase 2 PR)
3. notice Yahoo! JAPAN is at the bottom of Standard Tab under the search settings

Actual result

Desktop Example:

Example	Example

Android Example:

Expected result

As per the spec via https://github.com/brave/internal/issues/1227, Yahoo! JAPAN should be in the first position.

Reproduces how often

Easily reproduced

Desktop Brave version (brave://version info)

Brave | 1.78.61 Chromium: 135.0.7049.28 (Official Build) nightly (64-bit)
-- | --
Revision | 00759bb17d91e5ab1c85724a82eb466a626e4509
OS | Windows 11 Version 24H2 (Build 26100.3194)

Android device

• Brand/model: Pixel 6 Pro
• Android version: Android 15

Channel information

• release (stable)
• beta
• nightly

Reproducibility

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

Miscellaneous information

No response

[kjozwiak]

Going to remove the Desktop label as the work as split and @simonhong completed Desktop via #44923 which was already verified on 1.77.x.