When I stored my Model Y, I made sure to charge it to around 50% before parking it. It's generally best not to let the battery drain completely, as that can cause long-term damage.
I’ve used an electric cooler in my Model Y, and it plugs into the outlet in the back, drawing power directly from the main battery. Make sure to keep an eye on the cooler's power draw during your trip to avoid draining the battery too much.