Don't need to use the key on door?

[Frontcannon]

discarded bullshit I've written earlier

The CallbackFunc is used for something different entirely. It's immediately called once you interact wth the entity, so what happens is:

you pick up the key
KeyOnDoor is called, door unlocks
you are confused

The CallbackFunc of the door is just redundant now and will do nothing anymore, as for the AddUseItemCallback.
What ConnectedProp does is still new terrain to me either. Just delete everything what you've written in the callback and connectedporp boxes, your script is fine as is