### 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
if (bool(EDITOR_GET("run/output/always_clear_output_on_play"))) {
		log->clear();
	}
	if (bool(EDITOR_GET("run/output/always_open_output_on_play"))) {
		make_bottom_panel_item_visible(log);
	}
}
void EditorNode::_project_run_stopped() {
	if (!bool(EDITOR_GET("run/output/always_close_output_on_stop"))) {
		return;
	}
	for (int i = 0; i < bottom_panel_items.size(); i++) {
		if (bottom_panel_items[i].control == log) {
			_bottom_panel_switch(false, i);
			break;
		}
	}
}
void EditorNode::notify_all_debug_sessions_exited() {
	project_run_bar->stop_playing();
}
void EditorNode::add_io_error(const String &p_error) {
	DEV_ASSERT(Thread::get_caller_id() == Thread::get_main_id());
	singleton->load_errors->add_image(singleton->theme->get_icon(SNAME("Error"), EditorStringName(EditorIcons)));
	singleton->load_errors->add_text(p_error + "\n");
	EditorInterface::get_singleton()->popup_dialog_centered_ratio(singleton->load_error_dialog, 0.5);
}
void EditorNode::add_io_warning(const String &p_warning) {