feat(archy): wire archyBridge into app, base-aware API paths, nginx config

- Create useArchy composable wrapping archyBridge with reactive Vue state
- Initialize bridge in App.vue when ?embedded=true detected
- Inject Archy node context (apps, system, network) into AI system prompt
- Make API paths base-aware (import.meta.env.BASE_URL) for /aiui/ deployment
- Add nginx-archy.conf for production Anthropic API proxy with SSE support
- Fix archyBridge.ts typecheck error, export ActionResponse type

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

packages/app/src/adapters/claude-adapter.ts

@@ -1,7 +1,8 @@
 import type { AIAdapter, ChatMessage, ChatOptions } from './types'
 import { getApiKey } from '@/utils/key-vault'
 
-const CLAUDE_PATH = '/api/claude/v1/messages'
+const BASE = import.meta.env.BASE_URL || '/'
+const CLAUDE_PATH = `${BASE}api/claude/v1/messages`
 
 export const claudeAdapter: AIAdapter = {
   id: 'claude',