Hello,
another MicroE product 
When you check GSM-GPS click - schematic you can see there is a SIM808 module with some necessary components, leds, level convertor and finished with a MicroE MicroBbus.
So again there is not special commponents what can block direct communication with the module and SIM808 datasheet is usable and useful.
In the datasheet you can found the module is able to communicate via AT commands, which is easy. At the end of datasheet it refer to SIM808 AT Command Manual. It seems in this manual you can found all necessary commands for control of what you will need and also with a description.
In the basic you can use the Nucleo as UART repeater or a FTDI USB To TTL Serial Converter (If you have one) and send AT Commands directly from a PC Terminal for some testing.
For cooperation with Mbed you can use ATCmdParser - API references and tutorials | Mbed OS 6 Documentation
As some inspiration you can try to found some codes of another sides
- Sim808-Module-GSM-GPS-GPRS–Arduino-Interfacing-Code-With-Sensors-Involvement-as-well-/GSM_GPRS_CODE.ino at master · arpit-jadon/Sim808-Module-GSM-GPS-GPRS–Arduino-Interfacing-Code-With-Sensors-Involvement-as-well- (github.com)
- mikrosdk_click_v2/clicks/gsmgps at e95c758c2b7247ccc6cd5d43fdf4707dea8278f2 · MikroElektronika/mikrosdk_click_v2 (github.com)
- and more
BR, Jan