### 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)

String s = get_edited_property_value();
	property->set_text(s);
	selected_type = s;
}
void EditorPropertyClassName::_property_selected() {
	dialog->popup_create(true);
}
void EditorPropertyClassName::_dialog_created() {
	selected_type = dialog->get_selected_type();
	emit_changed(get_edited_property(), selected_type);
	update_property();
}
void EditorPropertyClassName::_bind_methods() {
}
EditorPropertyClassName::EditorPropertyClassName() {
	property = memnew(Button);
	property->set_clip_text(true);
	add_child(property);
	add_focusable(property);
	property->set_text(selected_type);
	property->connect("pressed", callable_mp(this, &EditorPropertyClassName::_property_selected));
	dialog = memnew(CreateDialog);
	dialog->set_base_type(base_type);
	dialog->connect("create", callable_mp(this, &EditorPropertyClassName::_dialog_created));
	add_child(dialog);
}
void EditorPropertyCheck::_set_read_only(bool p_read_only) {