### 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
top_split->set_visible(!p_pressed);
}
void EditorNode::_update_renderer_color() {
	String rendering_method = renderer->get_selected_metadata();
	if (rendering_method == "forward_plus") {
		renderer->add_theme_color_override("font_color", Color::hex(0x5d8c3fff));
	}
	if (rendering_method == "mobile") {
		renderer->add_theme_color_override("font_color", Color::hex(0xa5557dff));
	}
	if (rendering_method == "gl_compatibility") {
		renderer->add_theme_color_override("font_color", Color::hex(0x5586a4ff));
	}
}
void EditorNode::_renderer_selected(int p_which) {
	String rendering_method = renderer->get_item_metadata(p_which);
	String current_renderer = GLOBAL_GET("rendering/renderer/rendering_method");
	if (rendering_method == current_renderer) {
		return;
	}
	renderer_request = rendering_method;
	video_restart_dialog->popup_centered();
	renderer->select(renderer_current);
	_update_renderer_color();
}
void EditorNode::_add_renderer_entry(const String &p_renderer_name, bool p_mark_overridden) {