Hello dear,it is good to see this type of question on this platform.I want to say that the wire is uncharged as a charged conductor is that which has charge stored in its surface but a wire carrying current is just having a flow of electrons inside it.So ,it can not be considered as charged.Now,as you can see in a charged parallel plate capacitor you have charged plates which have accumulated charge on them.
Hope i am clear to you.

Hello sir, myself vanshika Sharma. Wire carrying current can be said to charged because charge are of 2 types (1) - static means charges are in rest and (2) - current means charges are in motion.