### Godot version

4.1.dev4

### System information

Windows 10 Godot 4.1.dev4

### Issue description

The watched property in the Multiplayer Synchronizer node is supposed to pass the variable through the network only when it changes, but as I use the network profiler, it is evidently not working as intended

### Steps to reproduce

Open 2 debug instances on the project I will give, use the network profiler and you will see the variable does not change, although it goes up to 780b/s on the network

### Minimal reproduction project

[minimalproject.zip](https://github.com/godotengine/godot/files/11659414/minimalproject.zip)

#include "scene_replication_config.h"
#include "scene/main/multiplayer_api.h"
#include "scene/main/node.h"
bool SceneReplicationConfig::_set(const StringName &p_name, const Variant &p_value) {
	String prop_name = p_name;
	if (prop_name.begins_with("properties/")) {
		int idx = prop_name.get_slicec('/', 1).to_int();
		String what = prop_name.get_slicec('/', 2);
		if (properties.size() == idx && what == "path") {
			ERR_FAIL_COND_V(p_value.get_type() != Variant::NODE_PATH, false);
			NodePath path = p_value;
			ERR_FAIL_COND_V(path.is_empty() || path.get_subname_count() == 0, false);
			add_property(path);
			return true;
		}
		ERR_FAIL_COND_V(p_value.get_type() != Variant::BOOL, false);
		ERR_FAIL_INDEX_V(idx, properties.size(), false);
		ReplicationProperty &prop = properties[idx];
		if (what == "sync") {
			if ((bool)p_value == prop.sync) {
				return true;
			}
			prop.sync = p_value;