Use Zustand store; modularize API & routes

Introduce a centralized Zustand store and refactor app state out of App.tsx into src/store/appStore.ts. Modularize API surface by moving media/cast/settings/converters/types into src/lib/api/* and re-exporting from src/api.ts for backward compatibility. Replace inline route helpers with dedicated route components (MediaDetailRoute, CastDetailRoute, CategoryBrowseRoute) and wire CATEGORY_PATHS/PATH_TO_CATEGORY constants. Update AddMediaView UI (icons, layout) and adjust settings/category handling to use DEFAULT_SETTINGS and the store. Add zustand to package.json/package-lock.json and include a new React SKILL.md. Overall changes improve state management, API organization, and route/component separation for better maintainability and code-splitting.

package-lock.json

@@ -25,7 +25,8 @@
         "shadcn": "^4.2.0",
         "tailwind-merge": "^3.5.0",
         "tw-animate-css": "^1.4.0",
-        "vite": "^6.2.0"
+        "vite": "^6.2.0",
+        "zustand": "^5.0.12"
       },
       "devDependencies": {
         "@types/express": "^4.17.21",
@@ -7611,6 +7612,35 @@
       "peerDependencies": {
         "zod": "^3.25.28 || ^4"
       }
+    },
+    "node_modules/zustand": {
+      "version": "5.0.12",
+      "resolved": "https://registry.npmjs.org/zustand/-/zustand-5.0.12.tgz",
+      "integrity": "sha512-i77ae3aZq4dhMlRhJVCYgMLKuSiZAaUPAct2AksxQ+gOtimhGMdXljRT21P5BNpeT4kXlLIckvkPM029OljD7g==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=12.20.0"
+      },
+      "peerDependencies": {
+        "@types/react": ">=18.0.0",
+        "immer": ">=9.0.6",
+        "react": ">=18.0.0",
+        "use-sync-external-store": ">=1.2.0"
+      },
+      "peerDependenciesMeta": {
+        "@types/react": {
+          "optional": true
+        },
+        "immer": {
+          "optional": true
+        },
+        "react": {
+          "optional": true
+        },
+        "use-sync-external-store": {
+          "optional": true
+        }
+      }
     }
   }
 }