[Follow up to #<issue number>] The icon for custom SE gets blank after Title is updated

[hffvld]

Description

Follow-up to #39552.

Steps to reproduce

1. Launch Brave
2. Hamburger menu > Settings
3. Search Engines > Add Custom Search Engine
4. In URL type https://youtube.com/search?q=%s and in Title type YT > Done
5. Slide the newly created SE to the left > Tap Edit
6. Update the Title > Save the changes by tapping the button in the top right corner
7. Observe that the icon is blank now

Actual result

The icon for custom SE gets blank after Title is updated.

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Expected result

The icon for custom SE must not be blank after updating the Title.

Reproduces how often

Easily reproduced

Brave version

Brave build: 1.70 (117)
BraveCore: 1.70.117 (129.0.6668.59)

Device/iOS version

iPad Mni (6th gen) / iPadOS 18

Affected browser versions

• latest AppStore
• latest TestFlight
• previous TestFlight

Reproducibility

• with Brave Shields disabled
• in the latest version of mobile Safari

Miscellaneous information

No response