### 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)

float ifl = i / float(point_count);
		const float h = 1.0 - Math::ease(ifl, exp);
		if (flip) {
			ifl = 1.0 - ifl;
		}
		points.push_back(Point2(ifl * s.width, h * s.height));
	}
	easing_draw->draw_polyline(points, line_color, 1.0, true);
	
	int decimals;
	if (Math::abs(exp) < 0.1 - CMP_EPSILON) {
		decimals = 4;
	} else if (Math::abs(exp) < 1 - CMP_EPSILON) {
		decimals = 3;
	} else if (Math::abs(exp) < 10 - CMP_EPSILON) {
		decimals = 2;
	} else {
		decimals = 1;
	}
	f->draw_string(ci, Point2(10, 10 + f->get_ascent(font_size)), TS->format_number(rtos(exp).pad_decimals(decimals)), HORIZONTAL_ALIGNMENT_LEFT, -1, font_size, font_color);
}
void EditorPropertyEasing::update_property() {
	easing_draw->queue_redraw();
}
void EditorPropertyEasing::_set_preset(int p_preset) {
	static const float preset_value[EASING_MAX] = { 0.0, 1.0, 2.0, 0.5, -2.0, -0.5 };
	emit_changed(get_edited_property(), preset_value[p_preset]);
	easing_draw->queue_redraw();
}
void EditorPropertyEasing::_setup_spin() {