feat: complete AIUI integration — all 31 overnight tasks

- Protocol: 10 context categories (apps, system, network, bitcoin, media, files, notes, search, ai-local, wallet)
- ContextBroker: real data wiring for all categories with sanitization
- Permissions: user toggles for all categories in Settings
- Nginx: Claude API, OpenRouter, SearXNG proxy pass-through
- Actions: launch-app, search-web, install-app handlers
- Chat.vue: loading state + connection indicator
- Integration test page: test-aiui.html

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

neode-ui/src/views/Marketplace.vue

@@ -118,7 +118,7 @@
     </div>
 
     <!-- Scrollable Apps Section -->
-    <div class="flex-1 overflow-y-auto pr-2 -mr-2 pb-0 md:pb-6">
+    <div class="flex-1 overflow-y-auto pr-2 -mr-2 pb-48">
       <!-- Apps Grid -->
     <div class="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-6">
       <div