Which connection type is used when an engineer connects to an AP without a configured IP address or dial-up number to manage the device?

An AUX (auxiliary) port is typically used for connecting a modem for out-of-band management via dial-up, which is explicitly ruled out by the question.

An Ethernet connection requires the AP to have an IP address and network connectivity to be managed, which contradicts the scenario described.

VIY is not a standard network connection type for device management.

The console port provides direct serial access to a device's command-line interface, making it the standard method for initial configuration, troubleshooting, and management of an AP when it does not have an IP address configured or when network connectivity is unavailable.