In order to make the MoveComponentTo function replicated in Unreal Engine, you will need to use the ReplicatedMovement property, which can be checked in the Replication section when selecting the Root component of your blueprint actor.
It is designed to replicate the transform data of the root component of an actor. For the flag to work, you need to ensure the actor is fully set to replicate and that it’s not sleeping.
For the jittery movement during interpolation, you may want to increase the NetUpdateFrequency variable. This will reduce the frequency of updates and smooth out the movement. This is done in the same menu where you changed the Replicate Movement.
I hope this is helpful!