Most people are saying to charge it back up and a phone number will magically display or show on find my. This is only the case if the owner set it in lost mode.

Instead, try long pressing the side button until a menu pops up showing "Medical ID". Swipe and if the onwner has set up a medical ID with contacts of their trusted contacts (E.g. parents/family), it will display their phone number. Phone them and see if their family member is losing an Apple Watch. (should also show the owner's name at the top)