Add basic conversation management controls to browser extension

[GeorgeNgMsft]

Browser extension: @conversation management parity

Bring the browser extension's chat panel to feature parity with the
Shell and CLI for conversation management.

What's new

• @conversation slash commands and natural-language phrases work in
  the browser chat panel: new, list, info, switch, prev,
  next, rename, delete.
• Switching a conversation clears the panel and replays the new
  conversation's history.
• Display events from peer clients (Shell or CLI joined to the same
  conversation) are now visible in the browser panel.

How

A new chatPanelManageConversation RPC bridges the dispatcher's
manage-conversation action from the chat panel to the service
worker, which implements the eight subcommands against the existing
agent-server APIs. Switching follows the bind-new → leave-old →
delete-old ordering used by the CLI to keep the user functional on
errors. A replay gate queues live display events during history reload
so they render in order.