Add bookmarks popup flickering in the URL bar

[GeetaSarvadnya]

Description

Add bookmarks popup flickering in the URL bar

Steps to Reproduce

1. Clean profile 1.41.x or 1.42.x
2. Enter hello in the URL bar
3. Open the 1st video from the seach results
4. Click on the bookmarks icon the URL bar
5. Add bookmarks popup starts flickering

Actual result:

Expected result:

Should not be any flickering

Reproduces how often:

Easy

Brave version (brave://version info)

Brave	1.42.73 Chromium: 103.0.5060.134 (Official Build) beta (64-bit)
Revision	8ec6fce403b3feb0869b0732eda8bd95011d333c-refs/branch-heads/5060@{#1262}
OS	Windows 10 Version 21H2 (Build 19044.1826)

Version/Channel Information:

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

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? NA
• Does the issue resolve itself when disabling Brave Rewards? NA
• Is the issue reproducible on the latest version of Chrome? No

Miscellaneous Information:

cc: @brave/legacy_qa @rebron