fix: enhance transport graceful shutdown with proper writer closure

[linw1995]

• Add TransportWriter type alias for cleaner type definitions
• Wrap transport writer in Option to enable proper closure
• Implement close() method to drop writer and signal end of communication
• Update graceful_shutdown to close transport before waiting for process exit
• Improve error handling for closed transport state

Motivation and Context

I recently built an MCP stdio server that uses grcov for code coverage collection. During integration testing, I discovered that source coverage from the MCP server binary was not being generated.
After investigation, I found that LLVM profile data is not produced when an executable exits with an abnormal status.

How Has This Been Tested?

Yes. I try it out on my project.

• Before: Coverage data was missing due to abnormal exit status
• After: Coverage data is consistently generated and collected

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

Addresses the graceful shutdown improvements discussed in #347 and #364