Reconciles the wallet balance against the loyalty partner's counter for campaigns where the partner is the source of truth (Carrefour LOYALTY). Computes the delta between the partner counter and the local ledger balance, writes a sync ledger entry for the difference (if any), and returns the updated balance. For campaigns without a partner counter configured, returns the current ledger balance unchanged.

Requires the partner's X-User-Token for LOYALTY campaigns. The response shape matches GET /me/loyalty/ledger/balance so callers can treat it as a balance refresh.