### 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
ERR_FAIL_COND_V_MSG(p_class.is_empty(), nullptr, "Class name cannot be empty.");
	EditorData &ed = EditorNode::get_editor_data();
	
	if (p_script.is_valid()) {
		Ref<Texture2D> script_icon = ed.get_script_icon(p_script);
		if (script_icon.is_valid()) {
			return script_icon;
		}
		if (p_fallback_script_to_theme) {
			
			
			String script_class_name = p_script->get_language()->get_global_class_name(p_script->get_path());
			String base_type = ScriptServer::get_global_class_native_base(script_class_name);
			if (theme.is_valid() && theme->has_icon(base_type, EditorStringName(EditorIcons))) {
				return theme->get_icon(base_type, EditorStringName(EditorIcons));
			}
		}
	}
	
	
	
	Ref<Texture2D> ext_icon = ed.extension_class_get_icon(p_class);
	if (ext_icon.is_valid()) {