This is 2 Clients, no standalone or listen server, but is the same case for listen server for 2 players.
As you can see movement translation replicates, also Traversal replicates perfect.
but this reading of the right animation idle -> walking or to running or to change of direction... doesnt replicates correctly.
Could you explain how you managed to perfectly replicate the Traversal? maybe the solution for this is there.

Btw, I added some basic changes to the replication set up too, not using PlayerController of index 0 and using RPCs for the Input to send to server and then multicast (as far as I know, this is the multiplayer approach):