[Follow up to #32843] YT search is not shown in QSE toolbar and settings screen for the upgraded profile

[hffvld]

Description

Follow-up to #32843.

Steps to reproduce

1. Install Brave Beta 1.74.10 (it was previously available in the Play Store)
2. Go through onboarding
3. Open NTP
4. Tap in the URL search bar > Type a query > Observe that YT search thumbnail is not shown
5. Tap ⚙️ icon > Observe that YT search is not shown
6. Upgrade Brave to Beta 1.74.13 or higher
7. Launch Brave > Type a query again > Observe that YT search thumbnail is NOT shown
8. Tap ⚙️ icon > Observe that YT is NOT shown

Actual result

YT search is not shown in the QSE toolbar and settings screen for the upgraded profile.

---

2024-11-27_12-23-26.mp4

Expected result

YT search must shown in the QSE toolbar and settings screen for the upgraded profile.

Reproduces how often

Easily reproduced

Brave version

Brave build: 1.74.13
Chromium: 131.0.6778.85 (Official Build) beta (64-bit)

Device

• Brand/model: ANY
• Android version: ANY

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