feat(chat): quick-action buttons in empty chat state (#363)

[dolho]

Closes #363.

Summary

• New ChatEmptyState.vue shared component renders up to 6 playbook buttons (or 4 fallback prompts when the agent has no playbooks).
• Wired into ChatPanel (authed agent chat) via the <ChatMessages> #empty slot.
• Wired into PublicChat above the input, gated on userMessageCount === 0 so the buttons coexist with the assistant intro message and disappear after the first user submit.
• Click behaviour:
  • Playbook without argument_hint → sends /<name> immediately (low friction — that's the point of a slash command).
  • Playbook with argument_hint → populates input so the user can fill the argument.
  • Fallback prompts → populate input.

Why

Paradigm Life client feedback: "Blank canvas after intro — no guidance." High activation energy for new/occasional users. Buttons surface 4-6 concrete things the agent can do.

Test plan

• Authed agent with playbooks (e.g. blank-agent injected with 4 test skills) → buttons render with playbook descriptions.
• Authed agent with zero playbooks (e.g. trinity-system) → 4 fallback prompts render.
• Click playbook without argument_hint → message sent immediately.
• Click playbook with argument_hint → input is populated, input area is focused, message is not sent.
• Click fallback prompt → input is populated, message not sent.
• Public link with intro → intro renders, quick-action buttons remain visible until first user message.
• After first user message, buttons disappear.
• Build is green (vite build, verified locally).

🤖 Generated with Claude Code

[dolho]