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/Cargo.toml

@@ -15,6 +15,7 @@ tauri-build = { version = "2", features = [] }
 [dependencies]
 tauri = { version = "2", features = [] }
 tauri-plugin-opener = "2"
+tauri-plugin-store = "2"
 serde = { version = "1", features = ["derive"] }
 serde_json = "1"
 easy-nostr = { path = "./easy-nostr" }