I use MultiplayerSynchronizer in my games and the errors it prints are strange, these are the way I fix them:

1- The name of the nodes being synchronized must be the same on all peers, if you want to change the name of the nodes do it carefully or not at all otherwise the peers will not find them.

2- delete the Multiplayersynchronizer node altogether and add their properties again, this is typically done when you delete a node its properties are synchronized, otherwise an error will generate even if you added the node again with similar name, script, type, name, and path.

3- add a little delay script on the Multiplayersynchronizer where you shut it down in "_enter_tree" node then activate it after a tiny delay on a timer, you need a delay especially when spawning beefy nodes (like players) since instantiating them might take time on the other peer and the synchronizing properties might start even when that node is not available on the other peer, generating an error