docs: translate to English, upgrade VitePress 1.6.4, add API reference

- Upgrade VitePress from 1.0.0-rc.4 to 1.6.4 (stable)
- Update all dependencies (vue 3.5, typescript 5.6, @vue/tsconfig 0.5)
- Remove defunct Documate AI integration and google-analytics plugin
- Add Google Analytics via head config instead
- Translate all 25+ documentation pages from Chinese to English
- Add comprehensive REST API reference (docs/api/index.md)
- Add v3.2 changelog to sidebar navigation (fixes dead link)
- Update version string from v3.1 to v3.2
- Fix homepage changelog link to point to v3.2
- Update all WebUI screenshots with current v3.2 UI
- Add new screenshots: calendar view, bangumi poster wall
- Remove obsolete files: documate.json, deploy/windows.md, deploy/unix.md
- Update CSS variables for VitePress 1.6.x compatibility

Generated with [Claude Code](https://claude.ai/code)
via [Happy](https://happy.engineering)

Co-Authored-By: Claude <noreply@anthropic.com>
Co-Authored-By: Happy <yesreply@happy.engineering>

docs/package.json

@@ -2,23 +2,15 @@
   "private": true,
   "scripts": {
     "docs:dev": "vitepress dev",
-    "docs:build": "vitepress build && mkdir -p .vitepress/dist/image && cp -rf image/icons .vitepress/dist/image/ && documate upload",
-    "docs:preview": "vitepress preview",
-    "deploy:preview": "vercel --cwd .vitepress/dist",
-    "documate:upload": "documate upload"
+    "docs:build": "vitepress build",
+    "docs:preview": "vitepress preview"
   },
   "devDependencies": {
-    "@documate/documate": "^0.2.1",
-    "@vue/tsconfig": "^0.4.0",
-    "medium-zoom": "^1.0.8",
-    "typescript": "4.9.5",
-    "vercel": "31.0.1",
-    "vitepress": "1.0.0-rc.4",
-    "vue": "3.3.4"
+    "@vue/tsconfig": "^0.5.1",
+    "medium-zoom": "^1.1.0",
+    "typescript": "~5.6.0",
+    "vitepress": "1.6.4",
+    "vue": "^3.5.0"
   },
-  "type": "module",
-  "dependencies": {
-    "@documate/vue": "^0.3.1",
-    "vitepress-plugin-google-analytics": "^1.0.2"
-  }
-}
+  "type": "module"
+}