Moves BraveMediaNotificationControllerServices class into a base module

[SergeyZhukovsky]

The PR moves BraveMediaNotificationControllerServices to the base module of bundles, similar to upstream's ChromeMediaNotificationControllerServices
Resolves brave/brave-browser#44302

Submitter Checklist:

• I confirm that no security/privacy review is needed and no other type of reviews are needed, or that I have requested them
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Squashed any review feedback or "fixup" commits before merge, so that history is a record of what happened in the repo, not your PR
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally:
  • npm run test -- brave_browser_tests, npm run test -- brave_unit_tests wiki
  • npm run presubmit wiki, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

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, 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/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

I couldn't replicate it. For some reason some devices require that some services were in the base module. That feature with Brave Talk keep mic and audio when phone is locked basically migrated through all channels, has been verified a few times and we didn't see any issues. To verify just simply make sure that Brave Talk meeting links are functional.

[SergeyZhukovsky]

@deeppandya we probably need to move it to the base module as well once feature is ready for release.

[deeppandya]

Thank you @SergeyZhukovsky

[AlexeyBarabash]

++

[samartnik]

lgtm

[deeppandya]

LGTM

[deeppandya]

Thank you @SergeyZhukovsky

[brave-builds]

Released in v1.78.7

[kjozwiak]

Verification PASSED on Pixel 6 Pro running Android 15 using the following build(s):

Brave | 1.78.7 Chromium: 134.0.6998.39 (Official Build) canary (64-bit)
--- | ---
Revision | 777512a9a91ee8924ddb909a5d25a86ef7fcd93f
OS | Android 15; Build/AP4A.250205.002; 35; REL

Using https://kjozwiak.github.io, clicked on several of the Brave Talk Links and ensured everything loaded without any issues. Also ensured that going to talk.brave.com and starting a Free Conversation/Call worked without issues as per the following:

screen-20250228-183159.mp4