feat(extension): inject public key into release zip to preserve Web Store extension ID (#1462)

The public key is hardcoded in vite.config.mts. When
SET_EXTENSION_PUBLIC_KEY_IN_MANIFEST is set, the vite build transforms
the copied manifest.json to include the key field, ensuring the packed
extension shares the same Chrome extension ID as the Web Store listing.

Fixes #1452

.github/workflows/publish.yml

@@ -135,6 +135,8 @@ jobs:
       - name: Build extension
         working-directory: ./packages/extension
         run: npm run build
+        env:
+          SET_EXTENSION_PUBLIC_KEY_IN_MANIFEST: 1
       - name: Get extension version
         id: get-version
         working-directory: ./packages/extension