### 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)

} else if (Object::cast_to<Node3D>(ret_nodes[n.parent])) {
							obj = memnew(Node3D);
#endif 
						}
					}
					if (!obj) {
						obj = memnew(Node);
					}
					node = Object::cast_to<Node>(obj);
				}
			}
		}
		if (node) {
			
			
			
			int nprop_count = n.properties.size();
			if (nprop_count) {
				const NodeData::Property *nprops = &n.properties[0];
				Dictionary missing_resource_properties;
				for (int j = 0; j < nprop_count; j++) {
					bool valid;
					ERR_FAIL_INDEX_V(nprops[j].value, prop_count, nullptr);
					if (nprops[j].name & FLAG_PATH_PROPERTY_IS_NODE) {
						uint32_t name_idx = nprops[j].name & (FLAG_PATH_PROPERTY_IS_NODE - 1);
						ERR_FAIL_UNSIGNED_INDEX_V(name_idx, (uint32_t)sname_count, nullptr);
						const StringName &prop_name = snames[name_idx];
						const Variant &prop_variant = props[nprops[j].value];
						if (prop_variant.get_type() == Variant::ARRAY) {
							if (Engine::get_singleton()->is_editor_hint()) {