The API requirements are HTTPS support, minimized bandwidth, and easy mobile integration.

• RESTful APIs (A) use HTTPS and are easy to integrate with mobile apps but use text-based formats like JSON, which are less efficient for bandwidth.
• MQTT (B) is lightweight (good for bandwidth) but is a messaging protocol, not HTTP-based, making HTTPS integration and API design more complex for mobile apps.
• gRPC (C) uses HTTP/2 (supports HTTPS), Protocol Buffers (binary, minimizing bandwidth), and offers strong client library support for mobile platforms, meeting all three requirements.
• SOAP (D) uses XML (high bandwidth) and is cumbersome for mobile integration.

gRPC-based APIs are optimal for balancing HTTPS support, bandwidth efficiency, and ease of mobile integration.