Cat and Glimmer are both creature types. Enduring Curiosity won't have those creature types when its last ability returns it to the battlefield because it won't be a creature.

A token that's a copy of Enduring Curiosity won't return to the battlefield when its last ability resolves.

If a nontoken permanent that's a copy of Enduring Curiosity dies while it's a creature, it will return to the battlefield as an enchantment when its last ability resolves. It won't have any card types other than enchantment.