You don’t need to replicate that.
See the default third person template for how they read whether a character is moving or not. All you need to do is read the velocity of the character, this is already updated on server and all clients, so if it’s greater than 0 then you can set your bool in the animation blueprint to true.
So basically, you can do everything you want here without any RPCs, RepNotifies, or Replicated variables.