### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
editor_data.clear_script_icon_cache();
	if (editor_data.get_edited_scene() == index) {
		
		_remove_edited_scene(p_change_tab);
	} else {
		
		editor_data.remove_scene(index);
	}
}
void EditorNode::set_edited_scene(Node *p_scene) {