unable to select Google as default SE for NTP search widget when 3 or more SEs are in the list

[LaurenWags]

Description

Found while testing https://github.com/brave/brave-browser/issues/41789

Unable to select Google as SE for NTP search widget when it's the first of 3 or more search engines.

Works fine on 1.73.91 (current release).

Steps to reproduce

1. Install 1.74.10
2. Close/relaunch to pull griffin
3. Open NTP
4. Click on Brave logo of search widget
5. Select "Customize List"
6. Select (in order): DDG, Google, Bing
7. De-select Brave
8. Close customize dashboard modal
9. Click on DDG logo on search widget
10. Click on Google from list ---> Google is not selected, remains DDG
11. Try selecting Bing from the list, this works fine
12. Now try selecting Google again --> Google is not selected but it switches to DDG

I considered maybe it was a problem with the first SE in the list, but if I use 3 different SEs (ex. DDG, Bing, Qwant), all 3 are selectable.

Actual result

https://github.com/user-attachments/assets/7c967b0e-3929-4b44-be63-b601ce074829

Expected result

Google should be able to be chosen like any other SE in the list. Here's an example with 3 different SEs and all can be chosen without issue:

https://github.com/user-attachments/assets/e289d195-6c4c-4f6d-9bcd-450bce90bd17

Reproduces how often

Easily reproduced

Brave version (brave://version info)

Brave	1.74.10 Chromium: 131.0.6778.85 (Official Build) beta (x86_64)
Revision	bdff9e7d7314280ddbce1c3ada3abee4ce4a3b32
OS	macOS Version 14.7.1 (Build 23H222)

Channel information

• [ ] release (stable)
• [x] beta
• [x] nightly

Reproducibility

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

Miscellaneous information

cc @rebron @IanKrieger @brave/qa-team

[MadhaviSeelam]

Reproduced this issue. Initially when I tested this I may have seen but I couldn't reproduce it because it appears to be order of selection matters.,

Select DDG or any other SE (Qwant) Select Google Will encounter above issue

Select Google SE first in the Dashboard then select any other SE (DDG, Qwant etc.) Switch between of them No issues selecting multiple SE

https://github.com/user-attachments/assets/399fa331-fcdc-4d11-9961-d4ffcae2f2fc