### 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)

spin->hide();
	
	dragging = false;
	easing_draw->queue_redraw();
}
void EditorPropertyEasing::setup(bool p_positive_only, bool p_flip) {
	flip = p_flip;
	positive_only = p_positive_only;
}
void EditorPropertyEasing::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_THEME_CHANGED:
		case NOTIFICATION_ENTER_TREE: {
			preset->clear();
			preset->add_icon_item(get_theme_icon(SNAME("CurveLinear"), SNAME("EditorIcons")), "Linear", EASING_LINEAR);
			preset->add_icon_item(get_theme_icon(SNAME("CurveIn"), SNAME("EditorIcons")), "Ease In", EASING_IN);
			preset->add_icon_item(get_theme_icon(SNAME("CurveOut"), SNAME("EditorIcons")), "Ease Out", EASING_OUT);
			preset->add_icon_item(get_theme_icon(SNAME("CurveConstant"), SNAME("EditorIcons")), "Zero", EASING_ZERO);
			if (!positive_only) {
				preset->add_icon_item(get_theme_icon(SNAME("CurveInOut"), SNAME("EditorIcons")), "Ease In-Out", EASING_IN_OUT);
				preset->add_icon_item(get_theme_icon(SNAME("CurveOutIn"), SNAME("EditorIcons")), "Ease Out-In", EASING_OUT_IN);
			}
			easing_draw->set_custom_minimum_size(Size2(0, get_theme_font(SNAME("font"), SNAME("Label"))->get_height(get_theme_font_size(SNAME("font_size"), SNAME("Label"))) * 2));
		} break;
	}
}
void EditorPropertyEasing::_bind_methods() {