[FEATURE] Expose VSCode debugger state (variables, call stack) to Claude

Currently, the Claude Code VSCode extension has access to the editor context (open files, selections) but has no visibility into the VSCode debugger runtime state. This means Claude cannot see:

• Variables pane (local/global variable values at a breakpoint)
• Call stack
• Watch expressions
• Debug console output
• Exception details at crash point

Use case

When debugging, a user has to manually copy/paste variable values or stack traces into the chat for Claude to help. If Claude could read this state directly, it could immediately suggest fixes without the user needing to relay runtime information manually.

Proposed solution

Integrate with the VSCode Debug Adapter Protocol to expose current debugger state as context when Claude is asked a question during a debug session.

Workaround today

Manually paste variable values / stack traces into the chat.