Upstream chain-of-activities coverage includes activities of business partners related to the production of goods or provision of services by the company. The recitals and Article 3 definition point to design, extraction, sourcing, manufacture, transport, storage, supply of raw materials, products or parts, and development of the product or service.
That is why a weak mapping limited to direct suppliers is not enough. The legal question is not whether the partner signs your contract, but whether the activity is connected to the company product or service in the covered part of the chain.