Lost Apple Watch

1. Look for your device on a map

To find your device, sign in to iCloud.com/find. Or use the Find My app on another Apple device that you own.

If your iPhone, iPad, or Apple Watch doesn’t appear in the list of devices, Find My was not turned on. But you can still protect your account if Find My was not turned on.

2.Mark as Lost

When you mark your device as lost, you remotely lock it with a passcode, keeping your information secure. This also disables Apple Pay on the missing device. And you can display a custom message with your contact information on the missing device. 

Mark your device as lost.

3.Report your missing device to local law enforcement

Law enforcement might request the serial number of your device. 

Find the serial number.

4.File a Theft and Loss claim

If your missing Watch is covered by AppleCare+ with Theft and Loss, file a claim for an iPhone replacement.

File a claim.

5.Remotely erase your device

If you erase a device that had iOS 15, iPadOS 15, or later installed, you can still use Find My to locate the device or play a sound on it. Otherwise, you won't be able to locate the device or play a sound after you erase it.

If you have AppleCare+ with Theft and Loss, do not erase your iPhone until your claim has been approved.

Erase your device.

6.Contact your wireless carrier

If the missing device is an iPhone or an iPad with cellular, report your missing device to your wireless carrier. Ask the carrier to disable your account to prevent calls, texts, and data use. And if your device is covered under your wireless carrier plan, file a claim.

7.Remove your missing device from your account

If you have AppleCare+ with Theft and Loss, do not remove your lost Watch from your account until your claim has been approved.

Go to appleid.apple.com to remove the missing device from your list of trusted devices.

See here - If your Apple Watch is lost or stolen - Apple Support