Hide Brave Rewards icon option requires a left-click on the Brave Rewards icon every time browser is restarted

[Tonev]

Description

Users can't use the new Hide Brave Rewards icon option without an extra left-click on the icon in advance. This is required after every browser restart.

Steps to Reproduce

1. Clean user profile in Brave Beta or Brave Nightly.
2. Right-click on the Brave Rewards icon in the address bar.

Actual result:

The Hide Brave Rewards icon option doesn't appear. For users to be able to use the option, they'll have to left-click on the Brave Rewards icon in the address bar, and then they'll be able to hide the icon through a right-click until they close the browser.

Expected result:

I would expect to be able to use the Hide Brave Rewards icon option with one click every time.

Reproduces how often:

100%

Brave version (brave://version info)

Brave	1.40.75 Chromium: 102.0.5005.61 (Official Build) beta (64-bit)
Revision	0e59bcc00cc4985ce39ad31c150065f159d95ad3-refs/branch-heads/5005@{#819}
OS	Windows 10 Version 21H2 (Build 19044.1706)

Brave	1.41.20 Chromium: 102.0.5005.61 (Official Build) nightly (64-bit)
Revision	0e59bcc00cc4985ce39ad31c150065f159d95ad3-refs/branch-heads/5005@{#819}
OS	Windows 10 Version 21H2 (Build 19044.1706)

Version/Channel Information:

• Can you reproduce this issue with the current release? N/A
• 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? N/A
• Does the issue resolve itself when disabling Brave Rewards? N/A
• Is the issue reproducible on the latest version of Chrome? N/A

Miscellaneous Information:

CC: @mkarolin @rebron

[Miyayes]

May be resolved for free with #22423

[Tonev]

@Miyayes

Isn't the linked issue supposed to introduce changes only when Brave Rewards is enabled?

[mkarolin]

This was addressed via #22423