### 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)

value = p_flag;
	queue_redraw();
}
void EditorPropertyLayersGrid::_bind_methods() {
	ADD_SIGNAL(MethodInfo("flag_changed", PropertyInfo(Variant::INT, "flag")));
	ADD_SIGNAL(MethodInfo("rename_confirmed", PropertyInfo(Variant::INT, "layer_id"), PropertyInfo(Variant::STRING, "new_name")));
}
void EditorPropertyLayers::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_ENTER_TREE:
		case NOTIFICATION_THEME_CHANGED: {
			button->set_texture_normal(get_theme_icon(SNAME("GuiTabMenuHl"), SNAME("EditorIcons")));
			button->set_texture_pressed(get_theme_icon(SNAME("GuiTabMenuHl"), SNAME("EditorIcons")));
			button->set_texture_disabled(get_theme_icon(SNAME("GuiTabMenu"), SNAME("EditorIcons")));
		} break;
	}
}
void EditorPropertyLayers::_set_read_only(bool p_read_only) {
	button->set_disabled(p_read_only);
	grid->set_read_only(p_read_only);
}
void EditorPropertyLayers::_grid_changed(uint32_t p_grid) {
	emit_changed(get_edited_property(), p_grid);
}
void EditorPropertyLayers::update_property() {
	uint32_t value = get_edited_property_value();
	grid->set_flag(value);
}
void EditorPropertyLayers::setup(LayerType p_layer_type) {