Refactor to Store-based architecture

- Create base Store class with private backend and protected getBackend()
- Add SettingsStore, ProviderKeysStore, SessionsStore
- Each store defines its own schema via getConfig()
- AppStorage now takes stores + backend in constructor
- Remove SessionsRepository (logic moved to SessionsStore)
- Update all consumers to use store API (storage.settings.get/set, storage.providerKeys.get/set)
- Update example app to follow new pattern: create stores, gather configs, create backend, wire
- Benefits: stores own their schema, no circular deps, cleaner separation

packages/web-ui/src/components/AgentInterface.ts

@@ -173,7 +173,7 @@ export class AgentInterface extends LitElement {
 
 		// Check if API key exists for the provider (only needed in direct mode)
 		const provider = session.state.model.provider;
-		const apiKey = await getAppStorage().getProviderKey(provider);
+		const apiKey = await getAppStorage().providerKeys.get(provider);
 
 		// If no API key, prompt for it
 		if (!apiKey) {