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A Covenant activated on Book of the Covenant is considered an Artifact and a Covenant.
no because it is being used as an artifact
It is being used as an Artifact. It is in a Fortress designed to hold Artifacts. It is staying on the table and having a lasting effect just like an Artifact. It is behaving in all the ways an Artifact acts and none of the ways an Enhancement acts.
Enhancements can't sit on the table and have lasting effects?
As a default, they cannot--the ones that do specify that they do.
Fine, what if I activate Book on the artifact pile, now its not in the temple.
And everyone making the wiseacre remarks about lingering Enhancements
Your idea is a valid idea, but the game simply does not give the option of activating a covenant as a covenant, there is no game rule that defines what that would mean.