Use BroadcastChannel API instead of window.opener to communicate between auth popup & original window

[MTG2000]

Replace the usage of window.opener in communicating auth state from callback with BroadcastChannel API

Motivation and Context

This changes solves this issue: #33 where basically some auth providers could be preventing the window.opener value from being preserved, so the auth flow won't be able to communicate the success/failure at the end.

How Has This Been Tested?

I tested it with our MCP server that had this problem, and the problem was solved.
Tested it with a couple of other MCP servers, and haven't seen any problems.
But feel free to test it in case I missed some edge case or there was a bug.

Breaking Changes

There shouldn't be any breaking changes.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed