feat(stdio): working directory support with validation and UX gating

[pavithrakamath]

• Add end-to-end workingDir support for stdio transport (client ↔ proxy)
• Server: /validate/working-dir endpoint and shared validator with unit tests
• Client: workingDir input, persisted state, copied config integration
• Client: useWorkingDirValidation hook; Connect awaits validation; disable while invalid/validating
• Tests: updated Sidebar jest, added server validator tests; unit suite passing; code formatted
• e2e note: no Playwright for workingDir yet due to proxy auth complexity

Motivation and Context

solves the issue (https://github.com/modelcontextprotocol/inspector/issues/718)

How Has This Been Tested?

Yes, connected to haiven-mcp-server using cwd

Breaking Changes

No

Types of changes

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

Checklist

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

Additional context