### 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)

if (n.instance >= 0 || n.type != TYPE_INSTANTIATED || i == 0) {
				
				if (i > 0) {
					if (parent) {
						parent->_add_child_nocheck(node, snames[n.name]);
						if (n.index >= 0 && n.index < parent->get_child_count() - 1) {
							parent->move_child(node, n.index);
						}
					} else {
						
						
						stray_instances.push_back(node); 
					}
				} else {
					if (Engine::get_singleton()->is_editor_hint()) {
						
						node->set_name(snames[n.name]);
					} else {
						node->_set_name_nocheck(snames[n.name]);
					}
				}
			}
			if (!old_parent_path.is_empty()) {
				node->_set_name_nocheck(old_parent_path + "@" + node->get_name());
			}
			if (n.owner >= 0) {
				NODE_FROM_ID(owner, n.owner);
				if (owner) {
					node->_set_owner_nocheck(owner);
					if (node->data.unique_name_in_owner) {