AWS IoT Core is the correct service for this scenario because it provides managed, secure device connectivity and messaging that can support large fleets and near real time exchanges between thermostats and cloud applications.

AWS IoT Core supports MQTT, WebSockets, and HTTP and it handles device authentication, authorization, and message routing at scale. The service offers a rules engine and device shadows so devices can publish and subscribe to topics and cloud applications can process or forward messages, which meets the requirement to securely exchange messages among 75,000 smart thermostats and other systems.

Amazon WorkSpaces is a cloud desktop service and it does not provide IoT device connectivity or messaging, so it is not suitable for this use case.

AWS Directory Service provides managed Active Directory for identity and access management and it is not designed for connecting or messaging IoT devices, so it does not meet the requirement.

AWS IoT Greengrass focuses on edge compute and local messaging for devices that need to run code or operate while offline and it complements rather than replaces AWS IoT Core for cloud connectivity.

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