stolen Apple Watch
my apple watch was stolen and it runs out of battery what can I do
Apple Watch Series 6
Follow the directions in this link, but honestly, there's not much you can do and once it's run out of battery, tracking it becomes impossible.
See the suggestions here --> If your Apple Watch is lost or stolen - Apple Support
Apple doesn't get involved in lost or stolen devices. And since the majority of stolen devices are never found, you'll likely be saving up to buy a replacement watch.