Driving the motion of shape keys with a rig, with a visual presentation and with keyframed bones of animated values is a preferable workflow for animators that involves drivers and an armature.
But when we put into question to how we can export that data outside of Blender with object-based shape keys, things become blurry and problematic, because the animation of said shape keys is stored within the armature as drivers.
Huzzah for Driver Exporter, which consists only of 2 buttons! Select the objects, have the animations as NLA strips and let the addon do the rest with freshly baked shape keys, which are no longer bound by armature limitations and lets them transfer easily to Unreal Engine 5, Unity and onwards.
If you want to utilize the maximum from drivers, check out DriverRig – https://inletzone.com/driverrig-shape-keys-to-bones
Inmix that with Master Shape Keys – https://inletzone.com/master-shape-keys-2
Category: Driver export utility
Blender: 2.93, 3.x, 4.x