Follow up of #24241 - Pin to taskbar from first run dialog

[MadhaviSeelam]

Description

Follow up of #24241 - Pin to taskbar from first run dialog

Steps to Reproduce

1. Follow steps from Pin to taskbar from first run dialog #24241 (comment)

Actual result:

Brave is not pinned to task bar after selecting to be a default browser

Expected result:

Brave should be pinned to taskbar

Ex1	Ex2

Reproduces how often:

Easily

Brave version (brave://version info)

Brave	1.44.12 Chromium: 104.0.5112.69 (Official Build) nightly (64-bit)
Revision	7ce2902023c722af8564068e6b26e934b83fd774-refs/branch-heads/5112@{#1213}
OS	Windows 11 Version 21H2 (Build 22000.795)

Version/Channel Information:

• Can you reproduce this issue with the current release? N/A
• Can you reproduce this issue with the beta channel? N/A
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields?
• Does the issue resolve itself when disabling Brave Rewards?
• Is the issue reproducible on the latest version of Chrome?

Miscellaneous Information:

@simonhong @rebron

[simonhong]

Set QA/No because this can be verified from #24241

[simonhong]

@MadhaviSeelam Please check again when nightly build has fix for this!