Add an AI agent API for Omarchy plugins

[ronald2wing]

Plugins can't cleanly use Omarchy's built-in agent, so each one rebuilds its own stack (keys, transport, security) — the exact stuff the security review warns against. It's already happening:

• cOMApilot — hand-rolled curl, keyring-stored API key, its own OpenAI/Anthropic/Ollama backends.
• omapilot — embeds a full coding-agent runtime (Pi) plus Codex/OpenCode harnesses.

They can call the Omarchy agent, but it's not usable: launching it pops up the AI tool window over the plugin, and the prompt-only route needs the API key re-supplied (the Omarchy agent's auth doesn't carry through). So they rebuild their own stacks.

The request: a headless JSON API for the agent — a plugin sends a JSON request (prompt + context), gets a structured JSON answer back in the background. No keys, no setup, no popup; the agent owns the key end-to-end. A secure way to use AI that passes the Omarchy marketplace's security review — "confirm once, then allow" is the proposed gate.

Capabilities: Chat (streaming) · JSON output · OS actions (via the agent's own prompts) · inter-plugin calls · permission levels ("answer only" vs. "can act").