When using the custom SSE request, the Authorization header can still be automatically attached to the SSE request.

Motivation and Context

Current:
When user customizes the initial SSE request, it will prevent an Authorization header from being automatically attached to the SSE request. It require user to fetch tokens from authProvider and set the Authorization header manually.
Ref:

Goal:
Simplify the code and reduce the risk of misuse.
There is an misused case: CherryHQ/cherry-studio#5709

How Has This Been Tested?

npm test -- src/client/sse.test.ts -t "refreshes expired token during SSE connection"

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

Additional context