Secondary Bar: Support Multiple Simultaneous AI Sessions Across Any AI Extension

Problem / Current Behavior

Right now, the Secondary Bar only shows one AI session at a time. This affects all AI extensions — not just one.

Examples of affected extensions:
• GitHub Copilot Chat
• Claude Code (VS Code)
• Any other AI chat extension

This causes two big problems:

• I lose context — When I switch sessions, the current conversation is gone
• Slow to reload — When I switch back, the AI reloads all context again from the start

Real example:
• Session A → Debugging a bug in auth.ts with GitHub Copilot
• I need to quickly ask Claude about writing tests for api.ts
• I switch → old Copilot session is gone
• I switch back → Copilot reloads all context again

This breaks focus and wastes time.

Desired Behavior

I want to keep multiple AI sessions open at the same time in the Secondary Bar.

Each session should:
• Stay active in the background
• Keep its own full conversation history
• Not reload context when I switch between sessions
• Work with any AI extension installed in VS Code

Why This Matters

• Developers work on multiple tasks at the same time
• Each task needs its own AI conversation and context
• Reloading context is slow and breaks focus
• This is a VS Code core feature — it should work for all AI tools, not just one

No implementation files, tests, or entry points are identified. Start by investigating how the VS Code Secondary Bar hosts AI extension sessions, including the session examples involving auth.ts and api.ts; done means multiple independent sessions remain active with their conversation history when switching between them.