If I follow these steps and then export selected objects or the scene, I get the mesh and the animation.

The best thing to do is just not put the armature into the collection, or if the collection isn't supposed to represent a single export, suppress it from the Exportables panel.

However if the scene isn't configured that way, then I accept that it's confusing that the animation isn't available for separate export. Perhaps armatures with animations should always be considered as exportables in their own right.