Device which went through `new onboarding` doesn't get `notification` when user uses `Send to your devices` on another device

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Description

A device that went through new onboarding doesn't get a notification when the user uses Send to your devices on another device.

Steps to reproduce

1. On an Android device enable experiment A via ADB: adb shell "echo '--enable-features=BraveDayZeroExperiment:variant/a' > /data/local/tmp/brave-test-day-zero-expt"
2. Fresh install and launch Brave
3. Go through onboarding
4. Join new or existing Sync chain
5. On another Android/iOS/Desktop device open any website
6. Use the Send to your device feature and select Android device with experiment A enabled
7. Send the link > Observe, no notification is seen

Actual result

A device that went through new onboarding doesn't get a notification when the user uses Send to your devices on another device.

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https://github.com/user-attachments/assets/fff120e7-a58e-409c-9adb-a00b9544950d

Expected result

Notification must be shown on a device when using Send to your devices from another user's device.

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https://github.com/user-attachments/assets/1c28dbee-929f-4271-b572-2a984fd979c3

Reproduces how often

Easily reproduced

Brave version

Brave build: 1.73.91 Chromium: 131.0.6778.85 (Official Build) (64-bit)

Device

• Brand/model: ANY
• Android version: ANY

Channel information

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

Reproducibility

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

Miscellaneous information

No response