chore: release v0.14.0

Bump root/backend/frontend to 0.14.0, move Unreleased notes under a dated
0.14.0 heading, and fix the stale README changelog badge (0.2.1 → 0.14.0).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/package.json

@@ -1,6 +1,6 @@
 {
   "name": "frontend",
-  "version": "0.13.1",
+  "version": "0.14.0",
   "private": true,
   "scripts": {
     "dev": "next dev",