The client spec should be the only config to be applied on the physical client side. Common specs take precedent on whichever physical side holds the logical server. As such, they can consider to be accurate when being applied to the logical server. A common spec should be used when applying to a logical server if it should modify all instances of the underlying world being played. If its a per world configuration, then a server config should take priority.
This is not true. This means that you are trying to execute logical server code on the logical client, which leads to desynchronization. If you really do need to sync the common configuration, you can send a packet. Here is also an unofficial version of the packet docs as well for more reference.