Add option to context-click remove Brave Rewards (BAT) icon

[stephendonner]

Description

No option to context-click remove Brave Rewards (BAT) icon, unlike Wallet and VPN icons

Steps to Reproduce

1. install 1.40.5
2. launch Brave
3. context-click on the Rewards (BAT) icon in the URL bar
4. context-click on the Wallet icon in the browser toolbar
5. enable VPN and SKUs SDKs via brave://flags
6. click on Relaunch to restart Brave
7. context-click on the VPN icon in the browser toolbar

Actual result:

We provide the ability to remove the Wallet and VPN icons via context-clicks, but not the Rewards/BAT icon.

Expected result:

Consistency - note you can remove it via Show Brave Rewards icon in address bar in brave://settings/appearance.

Also note the text differences already, in #22436.

Reproduces how often:

100%

Brave version (brave://version info)

Brave	1.40.5 Chromium: 101.0.4951.41 (Official Build) nightly (64-bit)
Revision	93c720db8323b3ec10d056025ab95c23a31997c9-refs/branch-heads/4951@{#904}
OS	Windows 10 Version 21H2 (Build 19044.1645)

cc @rebron @Miyayes @bsclifton

[Miyayes]

@mkarolin noted that we might've purposely disabled context menu/right click for icons that appear inside the address bar, and that it's our own code. That might've been intentional, so may need discussion about that functionality.

[mkarolin]

I looked back at the history here. We added a toggle in the settings to hide the icon in #2975, but it was - at the time - limited to when Rewards was disabled (when we had a Rewards on/off switch). When we removed the Rewards on/off switch in #11467 we also adjusted the toggle to always be able to hide the icon. Since we already have a way to hide it, there's no counterindication, IMO, to adding a way to do it via the context menu.

[mkarolin]

QA Plan:

1. Launch Brave
2. context-click on the Rewards (BAT) icon in the URL bar

Expected result:
Observe context menu with the option to hide the icon

3. Click on the menu option to hide the rewards icon

Expected result:
Rewards icon is no longer shown in the URL bar

4. Navigate to brave://settings/appearance

Expected result:
Confirm that Show Brave Rewards icon in address bar setting is OFF

5. Toggle Show Brave Rewards icon in address bar setting to ON

Expected result:
Rewards icon is shown in the URL bar

[GeetaSarvadnya]

Verification PASSED on

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)

• Verified the test plan from Add option to context-click remove Brave Rewards (BAT) icon #22525 (comment)
• Confirmed that the context menu is provided with the option to hide the Brave rewards icon
• Confirmed that the user can hide the rewards icon by clicking on the context menu
• Confirmed that after hiding the rewards icon is no longer shown in the URL bar
• Confirmed that the hide rewards settings retained across the tabs and windows
• Confirmed that hide rewards settings retained after the browser restart
• Confirmed that Show Brave Rewards icon in address bar settings is set to OFF in brave://settings/appearance
• Confirmed that the user can enable the switch Show Brave Rewards icon in the address bar
• Confirmed that the Brave rewards icon is shown in the URL bar after enabling the settings in brave://settings/appearance

[stephendonner]

Verified PASSED using

Brave	1.40.75 Chromium: 102.0.5005.61 (Official Build) beta (x86_64)
Revision	0e59bcc00cc4985ce39ad31c150065f159d95ad3-refs/branch-heads/5005@{#819}
OS	macOS Version 12.5 (Build 21G5027d)

• Verified the test plan from Add option to context-click remove Brave Rewards (BAT) icon #22525 (comment)
• Confirmed that the context menu is provided with the option to hide the Brave rewards icon
• Confirmed that the user can hide the rewards icon by clicking on the context menu
• Confirmed that after hiding the rewards icon is no longer shown in the URL bar
• Confirmed that the hide rewards settings retained across the tabs and windows
• Confirmed that hide rewards settings retained after the browser restart
• Confirmed that Show Brave Rewards icon in address bar settings is set to OFF in brave://settings/appearance
• Confirmed that the user can enable the switch Show Brave Rewards icon in the address bar
• Confirmed that the Brave rewards icon is shown in the URL bar after enabling the settings in brave://settings/appearance

[Tonev]

Filled #23124