Yeah. You can be both eager and anxious at the same time but they’re still conflicting emotions.
In fact you need two distinct words to convey the conflict of emotions sometimes. I’m sure astronauts on the launchpad are often both eager and anxious.
I believe the words anxious and anxiety are closely related.
It’s a relatively modern meaning of the word “anxious.” It is parallel to the way we might tell someone “worry about this, but not about that.”