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.