The drying crew has removed damaged materials. Who puts the house back together?

Check your scope: mitigation and reconstruction may be separate services, even when one company offers both. Ask who is responsible for source repair, rebuilding, permits and coordinating trades. Before handover, request the final drying records, photographs of concealed conditions and a list of remaining work. IICRC's public S500 description says correcting the water source is the owner's responsibility unless separately contracted. Agree on the rebuild scope and price rather than assuming it was included.