### 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)

checkbox->set_disabled(p_read_only);
}
void EditorPropertyCheck::_checkbox_pressed() {
	emit_changed(get_edited_property(), checkbox->is_pressed());
}
void EditorPropertyCheck::update_property() {
	bool c = get_edited_property_value();
	checkbox->set_pressed(c);
	checkbox->set_disabled(is_read_only());
}
void EditorPropertyCheck::_bind_methods() {
}
EditorPropertyCheck::EditorPropertyCheck() {
	checkbox = memnew(CheckBox);
	checkbox->set_text(TTR("On"));
	add_child(checkbox);
	add_focusable(checkbox);
	checkbox->connect("pressed", callable_mp(this, &EditorPropertyCheck::_checkbox_pressed));
}
void EditorPropertyEnum::_set_read_only(bool p_read_only) {
	options->set_disabled(p_read_only);
}
void EditorPropertyEnum::_option_selected(int p_which) {
	int64_t val = options->get_item_metadata(p_which);
	emit_changed(get_edited_property(), val);
}
void EditorPropertyEnum::update_property() {