Decide the nudge's count source and where it interjects in schema sync

## Question

Where does the nudge get the combined unique node+edge label count, and where in the schema sync flow does it interject to pause for confirmation?

Facts in hand (see map #2092): the Summary API is already fetched per connector and carries distinct-label counts; non-summary paths enumerate all labels before the expensive attribute-sampling loop; sync is TanStack-query driven; no blocking-modal pattern exists.

Decide:
- **Count source per backend** — Summary API counts vs. the label-enumeration fallback (Neptune-with-stats vs. without vs. generic Gremlin/openCypher/SPARQL endpoints).
- **Interjection point** — before a summary-based sync vs. after label enumeration / before attribute sampling.
- **How to pause** a query-driven sync while awaiting user confirmation.

---

> [!IMPORTANT]
> Internal only — this issue is maintained by the core team and is not accepting external contributions.

Start with map #2092, then trace the Summary API fetch and the non-summary label-enumeration path through the attribute-sampling loop. Review how the TanStack-query-driven schema sync is initiated and identify the existing confirmation or modal entry points. Done means the backend-specific count source, interjection point, and pause behavior are decided.

Written by the indexing model from the issue text.