[Follow up to #38340] Add Bookmark for <X> Tabs button shows wrong count when NTP is opened in background

[hffvld]

Description

Follow-up to #38340.

Steps to reproduce

1. Launch Brave
2. Open any 2 websites
3. Open 3 NTP > While on NTP tap and hold the Tab switch button > Confirm there is no Add Bookmark for <X> Tabs button
4. Keep NTP opened and switch to another tab with a random website opened
5. Tap and hold the Tab switch button > Tap Add Bookmark for 5 Tabs > Save
6. Open Bookmarks > Saved Tabs folder > Observe that only 2 tabs are saved

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2024-07-05_11-10-37.mp4

Actual result

The Add Bookmark for <X> Tabs button shows the wrong count when NTP is opened in the background.

Expected result

The correct number of tabs must be shown in the Add Bookmark for <X> Tabs button.

Reproduces how often

Easily reproduced

Brave version

Brave build: 1.68 (110)
BraveCore: 1.68.110 (127.0.6533.26)

Device/iOS version

iPhone 14 / iOS 17.6

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