### 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)

ERR_FAIL_COND_V(!sdata.is_valid(), nullptr);
			node = sdata->instantiate(p_edit_state == GEN_EDIT_STATE_DISABLED ? PackedScene::GEN_EDIT_STATE_DISABLED : PackedScene::GEN_EDIT_STATE_INSTANCE); 
			ERR_FAIL_COND_V(!node, nullptr);
			if (p_edit_state != GEN_EDIT_STATE_DISABLED) {
				node->set_scene_inherited_state(sdata->get_state());
			}
		} else if (n.instance >= 0) {
			
			if (n.instance & FLAG_INSTANCE_IS_PLACEHOLDER) {
				String scene_path = props[n.instance & FLAG_MASK];
				if (disable_placeholders) {
					Ref<PackedScene> sdata = ResourceLoader::load(scene_path, "PackedScene");
					ERR_FAIL_COND_V(!sdata.is_valid(), nullptr);
					node = sdata->instantiate(p_edit_state == GEN_EDIT_STATE_DISABLED ? PackedScene::GEN_EDIT_STATE_DISABLED : PackedScene::GEN_EDIT_STATE_INSTANCE);
					ERR_FAIL_COND_V(!node, nullptr);
				} else {
					InstancePlaceholder *ip = memnew(InstancePlaceholder);
					ip->set_instance_path(scene_path);
					node = ip;
				}
				node->set_scene_instance_load_placeholder(true);
			} else {
				Ref<PackedScene> sdata = props[n.instance & FLAG_MASK];
				ERR_FAIL_COND_V(!sdata.is_valid(), nullptr);
				node = sdata->instantiate(p_edit_state == GEN_EDIT_STATE_DISABLED ? PackedScene::GEN_EDIT_STATE_DISABLED : PackedScene::GEN_EDIT_STATE_INSTANCE);
				ERR_FAIL_COND_V(!node, nullptr);
			}
		} else if (n.type == TYPE_INSTANTIATED) {
			
			if (parent) {