feat: persist API keys across restarts via tauri-plugin-store

Keys are saved to keys.json in the app's private data directory
on both Linux and Android. load_keys is called on app mount to
restore them into NewsState before the first news fetch.

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

src-tauri/capabilities/default.json

@@ -5,6 +5,7 @@
   "windows": ["main"],
   "permissions": [
     "core:default",
-    "opener:default"
+    "opener:default",
+    "store:default"
   ]
 }