### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

Dictionary missing_resource_properties = p_node->get_meta(META_MISSING_RESOURCES, Dictionary());
	for (const PropertyInfo &E : plist) {
		if (!(E.usage & PROPERTY_USAGE_STORAGE)) {
			continue;
		}
		if (E.name == META_PROPERTY_MISSING_RESOURCES) {
			continue; 
		}
		if (E.name.begins_with(PackedScene::META_POINTER_PROPERTY_BASE)) {
			continue; 
		}
		
		if (!states_stack.is_empty()) {
			if ((E.usage & PROPERTY_USAGE_NO_INSTANCE_STATE)) {
				continue;
			}
		}
		StringName name = E.name;
		Variant value = p_node->get(name);
		bool use_deferred_node_path_bit = false;
		if (E.type == Variant::OBJECT && E.hint == PROPERTY_HINT_NODE_TYPE) {
			value = p_node->get(PackedScene::META_POINTER_PROPERTY_BASE + E.name);
			if (value.get_type() != Variant::NODE_PATH) {
				continue; 
			}
			use_deferred_node_path_bit = true;
		} else if (E.type == Variant::OBJECT && missing_resource_properties.has(E.name)) {
			
			Ref<Resource> ures = value;
			if (ures.is_null()) {