GLTF requires all animations per object to be pushed down and for all NLA tracks to have the same name in order for them to work. Obviously, this is not ideal to do by hand...
"Animation glTF allows multiple animations per file, with animations targeted to particular objects at time of export. To ensure that an animation is included, either (a) make it the active Action on the object, (b) create a single-strip NLA track, or (c) stash the action.
Only certain types of animation are supported:
Keyframe (translation, rotation, scale) Shape keys Armatures / skinning Animation of other properties, like lights or materials, will be ignored."