Add Anthropic prompt caching, pluggable storage, and CORS proxy support

Storage Architecture:
- New pluggable storage system with backends (LocalStorage, ChromeStorage, IndexedDB)
- SettingsRepository for app settings (proxy config, etc.)
- ProviderKeysRepository for API key management
- AppStorage with global accessors (getAppStorage, setAppStorage, initAppStorage)

Transport Refactoring:
- Renamed DirectTransport → ProviderTransport (calls LLM providers with optional CORS proxy)
- Renamed ProxyTransport → AppTransport (uses app server with user auth)
- Updated TransportMode: "direct" → "provider", "proxy" → "app"

CORS Proxy Integration:
- ProviderTransport checks proxy.enabled/proxy.url from storage
- When enabled, modifies model baseUrl to route through proxy: {proxyUrl}/?url={originalBaseUrl}
- ProviderKeyInput test function also honors proxy settings
- Settings dialog with Proxy tab (Switch toggle, URL input, explanatory description)

Anthropic Prompt Caching:
- System prompt cached with cache_control markers (both OAuth and regular API keys)
- Last user message cached to cache conversation history
- Saves 90% on input tokens for cached content (10x cost reduction)

Settings Dialog Improvements:
- Configurable tab system with SettingsTab base class
- ApiKeysTab and ProxyTab as custom elements
- Switch toggle for proxy enable (instead of Checkbox)
- Explanatory paragraphs for each tab
- ApiKeyPromptDialog reuses ProviderKeyInput component

Removed:
- Deprecated ApiKeysDialog (replaced by ProviderKeyInput in SettingsDialog)
- Old storage-adapter and key-store (replaced by new storage architecture)

packages/web-ui/src/storage/app-storage.ts

@@ -0,0 +1,53 @@
+import { LocalStorageBackend } from "./backends/local-storage-backend.js";
+import { ProviderKeysRepository } from "./repositories/provider-keys-repository.js";
+import { SettingsRepository } from "./repositories/settings-repository.js";
+import type { AppStorageConfig } from "./types.js";
+
+/**
+ * High-level storage API aggregating all repositories.
+ * Apps configure backends and use repositories through this interface.
+ */
+export class AppStorage {
+	readonly settings: SettingsRepository;
+	readonly providerKeys: ProviderKeysRepository;
+
+	constructor(config: AppStorageConfig = {}) {
+		// Use LocalStorage with prefixes as defaults
+		const settingsBackend = config.settings ?? new LocalStorageBackend("settings");
+		const providerKeysBackend = config.providerKeys ?? new LocalStorageBackend("providerKeys");
+
+		this.settings = new SettingsRepository(settingsBackend);
+		this.providerKeys = new ProviderKeysRepository(providerKeysBackend);
+	}
+}
+
+// Global instance management
+let globalAppStorage: AppStorage | null = null;
+
+/**
+ * Get the global AppStorage instance.
+ * Throws if not initialized.
+ */
+export function getAppStorage(): AppStorage {
+	if (!globalAppStorage) {
+		throw new Error("AppStorage not initialized. Call setAppStorage() first.");
+	}
+	return globalAppStorage;
+}
+
+/**
+ * Set the global AppStorage instance.
+ */
+export function setAppStorage(storage: AppStorage): void {
+	globalAppStorage = storage;
+}
+
+/**
+ * Initialize AppStorage with default configuration if not already set.
+ */
+export function initAppStorage(config: AppStorageConfig = {}): AppStorage {
+	if (!globalAppStorage) {
+		globalAppStorage = new AppStorage(config);
+	}
+	return globalAppStorage;
+}