This same issue (or something similar) happens to me with models I download from other people when I try to open them in blender and then export them as gltf.
There seems to be a weird bug where exporting in Blender ignores every animation on a newly imported model unless that animation has been selected at least once in blender, and in many cases I wouldn’t preview the animations in blender so it would only export the first animation that was selected by default. So to export them all I realized I just have to select each individual animation and play them at least once in blender before exporting and saving. And then it successfully exports all the animations without having to use the NLA track. So there definitely seems to be some bug there in blender.