Rewards button pre-opt-in badge dismisses after first button press

[petemill]

We use a new pref to store the "badge text" value. Whilst we could store a boolean value whose state would be "has dismissed notification" (or not), this method is more future proof for having multiple variations of badge text, especially if or when this button becomes 'native' all the time (i.e. not an extension icon where the badge is controlled via JS).

Fix brave/brave-browser#6691

Test plan

0. Clean user data directory
1. Launch Brave
2. Create a second profile via App Menu -> Create a New Profile
3. Expected: Both profile windows have the rewards icon with the badge text "1"
4. Click the rewards button in the second profile window
5. Expected: The second profile window's rewards icon does not have a badge
6. Expected: The first profile window's rewards icon does have a badge
7. Quit the browser
8. Start the browser again
9. Expected: The rewards icon badge state from each profile window is the same as 5) and 6)

Submitter Checklist:

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Verified that these changes build without errors on
  • Android
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that these changes pass automated tests (unit, browser, security tests) on
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that all lint errors/warnings are resolved (npm run lint)
• Ran git rebase master (if needed).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Request a security/privacy review as needed.
• Add appropriate QA labels (QA/Yes or QA/No) to include the closed issue in milestone
• Public documentation has been updated as necessary. For instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protection-Mode
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-compatibility-issues-with-tracking-protection
  • https://github.com/brave/brave-browser/wiki/QA-Guide

Test Plan:

Reviewer Checklist:

• New files have MPL-2.0 license header.
• Request a security/privacy review as needed.
• Adequate test coverage exists to prevent regressions
• Verify test plan is specified in PR before merging to source

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on.
• All relevant documentation has been updated.

[bsclifton]

Works beautifully! 😄👌

[bsclifton]

Restarted CI (there were some issues; thanks @linhkikuchi and @mihaiplesa for the help!). This next run should be accurate 👍