fix: send MCP initialize metadata for stdio backends

[hrntknr]

Summary

Ensure stdio-backed MCP initialization sends protocol version and client info, with a bounded init context to avoid premature exits.

Type of Change

• feat: A new feature
• fix: A bug fix
• docs: Documentation only changes
• style: Changes that do not affect the meaning of the code (white-space, formatting, missing semi-colons, etc)
• refactor: A code change that neither fixes a bug nor adds a feature
• perf: A code change that improves performance
• test: Adding missing tests or correcting existing tests
• build: Changes that affect the build system or external dependencies
• ci: Changes to our CI configuration files and scripts
• chore: Other changes that don't modify src or test files
• revert: Reverts a previous commit

Related Issues

[Copilot]

Pull request overview

This PR fixes the MCP initialization process for stdio backends by adding required protocol metadata and timeout handling. The change ensures proper client identification during the initialization handshake.

• Adds protocol version and client info to the initialization request
• Implements a bounded timeout context to prevent indefinite hangs during initialization

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[Copilot]

Hardcoded version string 'dev' should be replaced with an actual version variable or constant that can be updated during build time (e.g., via ldflags). This makes it easier to track which version of the proxy is being used in production.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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