chore: release v0.13.0

Bump version to 0.13.0 across root/backend/frontend, add the 0.13.0 CHANGELOG
entry, and refresh stale CLAUDE.md docs (the AI chat is real and @ai-sdk/react
is installed; the signing/approval flow is built).

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

package.json

@@ -1,6 +1,6 @@
 {
   "name": "temetro",
-  "version": "0.12.1",
+  "version": "0.13.0",
   "private": true,
   "devDependencies": {
     "shadcn": "^4.11.0"