Applicability should include third parties when they provide part of the trust service or a trust service component. EN 319 401 says a TSP that uses other parties, including trust service component providers, remains responsible for conformance with the supply chain policy, information security policy, and trust service policy requirements.
The source material supports a practical test: if the supplier, cloud service, subcontractor, or component can affect the trust service's security, functionality, availability, or policy conformance, it belongs in the applicability record. That does not make the supplier the TSP, but it does mean the TSP needs contractual, security, monitoring, lifecycle, and assurance evidence for the dependency.