Since you're not using a motherboard with OOB management, One option would be a network connected power strip or smart outlet. Many consumer motherboards have a setting to automatically boot back when power is restored after a power failure so you could just kill the power remotely and then the computer would turn on when you restored power.
either a smart outlet at the low end or something like this at the high end: https://www.amazon.com/dp/B0039OZKPE?ref_=cm_sw_r_cp_ud_dp_SBHJ0ZNWMV8E9GDAY88K
depends on what level of control you want.
Should I get one of these or a switched PDU like one of these? Is the interface for the web power switch for basic functions like the auto restart function managed through a web interface?
NP-05B Remote PDU, UL-STD TUV Listed, 5 Switchable Outlets. Manufactured and Supported in USA. Control Via Web, Telnet, USB Serial Port. https://smile.amazon.com/dp/B0039OZKPE/ref=cm_sw_r_cp_api_i_.z.pFbQF3XD45
I think I understand your use case. Have you considered something like this: https://www.amazon.com/Switched-Switchable-Outlets-Designed-Supported/dp/B0039OZKPE
If you need to plug / unplug the device you could use this to do that remotely.
Maybe if the offshore IT people were up to snuff they would have invested in https://www.amazon.com/Managed-Designed-Manufactured-Synaccess-Networks/dp/B0039OZKPE and its big brothers Every data center we use has monitored power.