Models of quartz crystal do not have transconductance. No equation nor explanation in the linked design guide demand the transconductance of a crystal.
Transconductance is a property of a fet amplifier in the oscillator part of the microcontroller. It can be found in the microcontroller datasheet. You can think of it with the next simplification of the oscillator amp:
RF (=feedback resistor) is several megaohms. The idle DC voltage at the Osc OUT pin and at the gate of M1 is about the same as the treshold voltage of fet M1.
If a small amplitude AC signal voltage Uin is summed to the DC at the gate of M1 the small signal transconductance Gm of M1 defines what AC current there occurs in the drain current of M1. It is Gm * Uin.
Because The biasing current source lets a certain DC current only, all AC current sucked by the fet occurs in the OscOUT wire. Thus the transconductance of the fet M1 can be seen as the transconductance of the oscillator amp.
NOTE: This is a simplification. Gm of a fet is not constant, it depends on the DC operating point which depends on the operating state of the microcontroller.
Add due a comment:
STM32F446RC datasheet doesn't have the transconductance of the crystal oscillator amp. It's not needed because they say it in other way. They specify the maximum allowed value for quantity Gmcrit which is a property of a crystal+its nominal load capacitance. That property is not in usual specs of the crystals, because it's taken into use in your linked oscillator design guide (page 13) by the writer of that guide. There it's calculated as follows:
If Gmcrit is allowed to be max. 1mA/V the Gm of the oscillator amp must be a few times bigger, say 5mA/V or more to have some margin and a plausible start of oscillation. You must calculate if your crystal has small enough Gmcrit.
