### 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)

option_button->set_h_size_flags(SIZE_EXPAND_FILL);
	option_button->set_clip_text(true);
	option_button->set_flat(true);
	option_button->set_auto_translate(false);
	default_layout->add_child(option_button);
	option_button->connect("item_selected", callable_mp(this, &EditorPropertyTextEnum::_option_selected));
	edit_button = memnew(Button);
	edit_button->set_flat(true);
	edit_button->hide();
	default_layout->add_child(edit_button);
	edit_button->connect("pressed", callable_mp(this, &EditorPropertyTextEnum::_edit_custom_value));
	custom_value_edit = memnew(LineEdit);
	custom_value_edit->set_h_size_flags(SIZE_EXPAND_FILL);
	edit_custom_layout->add_child(custom_value_edit);
	custom_value_edit->connect("text_submitted", callable_mp(this, &EditorPropertyTextEnum::_custom_value_submitted));
	accept_button = memnew(Button);
	accept_button->set_flat(true);
	edit_custom_layout->add_child(accept_button);
	accept_button->connect("pressed", callable_mp(this, &EditorPropertyTextEnum::_custom_value_accepted));
	cancel_button = memnew(Button);
	cancel_button->set_flat(true);
	edit_custom_layout->add_child(cancel_button);
	cancel_button->connect("pressed", callable_mp(this, &EditorPropertyTextEnum::_custom_value_canceled));
	add_focusable(option_button);
	add_focusable(edit_button);
	add_focusable(custom_value_edit);
	add_focusable(accept_button);
	add_focusable(cancel_button);
}
void EditorPropertyLocale::_locale_selected(const String &p_locale) {