Add web app manifest, bump version to 0.1.1

manifest.ts uses icon.svg and the app's palette for background/theme
color. Excluded /manifest.webmanifest from the auth gate in proxy.ts,
same as icon.svg/favicon.ico - it must be publicly fetchable regardless
of login state.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01W8WkFF5ppURBAB918593Eb

package.json

@@ -1,6 +1,6 @@
 {
   "name": "sexy",
-  "version": "0.1.0",
+  "version": "0.1.1",
   "private": true,
   "scripts": {
     "dev": "next dev",