Persists widget menus when they aren't in the foreground

[ryanml]

Fixes brave/brave-browser#10199, brave/brave-browser#10749

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-Protections
  • 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:

Defined in issue

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.

[emerick]

LGTM

[petemill]

Haven't had a chance to test but code looks pretty good!

[ryanml]

CI failures unrelated

[LaurenWags]

Verified brave/brave-browser#10749 using

Brave | 1.14.45 Chromium: 85.0.4183.69 (Build officiel) nightly (64 bits)
-- | --
Révision | 4554ea1a1171bd8d06951a4b7d9336afe6c59967-refs/branch-heads/4183@{#1426}
Système d'exploitation | macOS Version 10.14.6 (assemblage 18G3020)

• Verified STR outlined in [Desktop] some NTP widget menus do not look nice with translations brave-browser#10749 (comment)
• Spot checked the following languages:

French

German

English

[kjozwiak]

Verification re: https://github.com/brave/brave-browser/issues/10199

Verification PASSED on macOS 10.15.6 x64 using the following build:

Brave | 1.14.45 Chromium: 85.0.4183.69 (Official Build) nightly (64-bit)
-- | --
Revision | 4554ea1a1171bd8d06951a4b7d9336afe6c59967-refs/branch-heads/4183@{#1426}
OS | macOS Version 10.15.6 (Build 19G73)

• ensured that the STR/Cases outlined via [Desktop] Unable to use menu items for stacked widgets  brave-browser#10199 passed
• ensured that you can switch between Brave Rewards, Binance, Gemini and Brave Together widgets without any issues
• ensured that you can click menu the items on stacked widgets without running into [Desktop] Unable to use menu items for stacked widgets  brave-browser#10199
  • ensured that Hide, Disconnect, Learn More, Refresh all worked