It's a common issue :) You have to deparent them, give the player's position to the camera so that it can follow the player and make the camera follow the player's position with some dampening applied
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Yeah, but that'd only be part of it, since the movement would still jump around a ton. Better camera, but still annoying. The clean version would involve no longer syncing the player position, but instead syncing the grid position. While the player tweens between grid cells, there should be enough time to validate if that new position is a legal place for the player to be in or not, if it isn't the server can revert the movement before it reaches any other players.
Buuuuut it was a bit too late when we realized how annoying this issue actually becomes over greater distances.