The gateway is a small form-factor computer with a rechargeable battery, e.g., a netbook or laptop. The AP is a SBC that the preferred kernel, e.g., NetBSD, OpenBSD, Linux, etc., supports. The AP draws power from the gateway's battery via USB.

Regarding LTE modems, I do not use a data plan on "locked-down" mobile devices for personal use. Somehow I have been able to survive on WiFi alone.