Rename ChromeStorageBackend to WebExtensionStorageBackend for cross-browser support

- Rename chrome-storage-backend.ts to web-extension-storage-backend.ts
- Update to use globalThis.browser || globalThis.chrome for Firefox/Chrome compatibility
- Export both names for backward compatibility
- Fix tsc --preserveWatchOutput in web-ui dev script to prevent console clearing

This fixes the "browser is not defined" error in Chrome extensions.

packages/web-ui/package.json

@@ -12,7 +12,7 @@
   "scripts": {
     "clean": "rm -rf dist",
     "build": "tsc -p tsconfig.build.json && tailwindcss -i ./src/app.css -o ./dist/app.css --minify",
-    "dev": "concurrently --names \"build,example\" --prefix-colors \"cyan,green\" \"tsc -p tsconfig.build.json --watch\" \"tailwindcss -i ./src/app.css -o ./dist/app.css --watch\" \"npm run dev --prefix example\"",
+    "dev": "concurrently --names \"build,example\" --prefix-colors \"cyan,green\" \"tsc -p tsconfig.build.json --watch --preserveWatchOutput\" \"tailwindcss -i ./src/app.css -o ./dist/app.css --watch\" \"npm run dev --prefix example\"",
     "typecheck": "tsc --noEmit && cd example && tsc --noEmit",
     "check": "npm run typecheck"
   },