If I understand proxies correctly, it’s only Autonomous characters that are laggy/jittery, but only from the Host’s side (as for him everybody is autonomous proxy). Host sees himself fine, but all client’s characters are laggy/jittery. Meanwhile client sees everybody fine (including himself as Autonomous proxy).
So far the only progress I was able to achieve was setting bOnlyAllowAutonomousTickPose to false inside Character’s OnPossessBy function, which eliminated laggy/jittery animations on clients, but it also made them run 2 times as fast (the animations, actual movement speed is correct)
Also just to add, if Client has up to 30 fps animations on Host are also smooth, but if Client reaches around 10 fps, animations are pretty jittery on Host (client is an ancient laptop)