### 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 rel = mm->get_relative().x;
		if (rel == 0) {
			return;
		}
		if (flip) {
			rel = -rel;
		}
		float val = get_edited_property_value();
		bool sg = val < 0;
		val = Math::absf(val);
		val = Math::log(val) / Math::log((float)2.0);
		
		val += rel * 0.05;
		val = Math::pow(2.0f, val);
		if (sg) {
			val = -val;
		}
		
		
		if (Math::is_zero_approx(val)) {
			val = 0.00001;
		}
		
		
		val = CLAMP(val, -1'000'000, 1'000'000);
		emit_changed(get_edited_property(), val);
		easing_draw->queue_redraw();
	}
}
void EditorPropertyEasing::_draw_easing() {