One layer down from where this thread is looking: the SMS never lives in the Android userspace on these sticks. It sits in the modem's own store, either on the SIM or in modem memory, and the vendor web UI is just a thin thing reading it out of there.

So you don't need a messaging app that still runs on Android 4.x. If the device exposes an AT port, AT+CMGF=1 then AT+CMGL="ALL" dumps everything, and AT+CPMS picks which store you're reading. On the Qualcomm ones that keep the AT port hidden behind QMI, libqmi reaches the same thing through the WMS service.