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/composables/useAI.ts

@@ -5,11 +5,14 @@ import { getApiKey } from '@/utils/key-vault'
 import type { ImageAttachment } from '@aiui/core/types/message'
 import { usePersonaStore } from '@/stores/personas'
 import { useMemoryStore } from '@/stores/memory'
+import { useArchy } from '@/composables/useArchy'
 
 type Provider = 'claude' | 'openrouter' | 'mock'
 
-const CLAUDE_PATH = '/api/claude/v1/messages'
-const OPENROUTER_PATH = '/api/openrouter'
+// API paths are relative to the base URL so they work both in dev (/) and Archy (/aiui/)
+const BASE = import.meta.env.BASE_URL || '/'
+const CLAUDE_PATH = `${BASE}api/claude/v1/messages`
+const OPENROUTER_PATH = `${BASE}api/openrouter`
 
 import { mockFilms } from '@/mocks/films'
 import { mockSongs } from '@/mocks/songs'
@@ -343,6 +346,10 @@ function buildSystemPrompt(chatStore: ReturnType<typeof useChatStore>): string {
 **Web search:** You have access to WebSearch and WebFetch tools. Use them to look up current information, news, and facts when the user asks. You can search the web and fetch page content. Web search is enabled for this session—do not tell the user it is unavailable.`
   }
 
+  // Append Archy node context when running embedded in Archipelago
+  const archy = useArchy()
+  prompt += archy.buildArchyContext()
+
   return prompt
 }