### 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)

use_sub_inspector = bool(EDITOR_GET("interface/inspector/open_resources_in_current_inspector"));
}
bool EditorInspectorDefaultPlugin::can_handle(Object *p_object) {
	return true; 
}
bool EditorInspectorDefaultPlugin::parse_property(Object *p_object, const Variant::Type p_type, const String &p_path, const PropertyHint p_hint, const String &p_hint_text, const BitField<PropertyUsageFlags> p_usage, const bool p_wide) {
	Control *editor = EditorInspectorDefaultPlugin::get_editor_for_property(p_object, p_type, p_path, p_hint, p_hint_text, p_usage, p_wide);
	if (editor) {
		add_property_editor(p_path, editor);
	}
	return false;
}
struct EditorPropertyRangeHint {
	bool or_greater = true;
	bool or_less = true;
	double min = -99999.0;
	double max = 99999.0;
	double step = 1.0;
	String suffix;
	bool exp_range = false;
	bool hide_slider = true;
	bool radians = false;
};
static EditorPropertyRangeHint _parse_range_hint(PropertyHint p_hint, const String &p_hint_text, double p_default_step, bool is_int = false) {