Rename public partner API identifier

[dawoodali-showpass]

Summary

Rename the public Partner API customer identifier from partner_user_id to partner_external_user_id.

Changes

• Update Partner API documentation, request examples, response examples, and webhook documentation.
• Regenerate the documentation search index.
• Keep the change limited to the public contract rename; no API Explorer or unrelated documentation changes are included.

Validation

• npm run test
• npx tsc -p tsconfig.app.json --noEmit
• npm run build
• git diff --check

The build completed with the repository's existing Browserslist, Vite glob, and chunk-size warnings.