Fix chat surface filtering, responsive controls, and launch context

[selfcontained]

Summary

• reliably hide all child-agent traffic when the child-message filter is off
• compact and animate the Chat/Console control, align its filter button, and hide it for terminal or disconnected panes
• constrain mobile chat content and keep wide Markdown tables scrollable
• separate user launch context from generated runtime guidance and shorten the Chat reply envelope

Validation

• pnpm run check
• pnpm run finalize:web
• pnpm run test
• pnpm run test:e2e (196 passed, 13 skipped)
• frontend UX review: all findings resolved
• backend security review: all findings resolved
• human review: resolved