Bug description:
exporting gltf with Blender 3.6.16. plugin 0.3.4, with some animated material in the NLA track (playing animation in Blender), no sign of animated stuff in the gltf, thus no animation in game
The issue happen because you are using two UV offset animations in the same time, while the game engine currently support only one.
To resolve this, clear the keyframes for the UV Offset V (set to 0 in your sample), leaving only the UV Offset U. This will allow the animation to work in-game.
I have also logged an issue regarding the lack of support for both UV offset animations.