Hi jnklz,
We'd like to assist. While we're not entirely sure what you're seeing regarding the Watch utility that you mentioned, we do have some information to share about Find My. If you don't see your Apple Watch as a device there, it might not have had Find My turned on before it went missing. However, this guidance is worth reviewing If your device is lost or stolen:
"If you can't find your Apple Watch
If you didn't turn on Find My before your Apple Watch was lost or stolen and your watch isn't connected to Wi-Fi, cellular, or your paired iPhone, you can't use it to find your device. However, you can use these steps to help protect your information:
- Place your Apple Watch in Lost Mode. When your watch is in Lost Mode, your passcode is required before anyone can turn off Find My, erase your watch, or pair it with another iPhone.
- Change your Apple ID password. When you change your Apple ID password, you can prevent anyone from accessing your iCloud information or from using other services from your missing device.
- Report your lost or stolen device to local law enforcement. Law enforcement might request the serial number of your device. Find your device serial number.
Find My is the only way that you can track or locate a lost or missing device. If Find My isn't enabled on your watch before it goes missing, there is no other Apple service that can find, track, or otherwise flag your device for you."
We hope this helps. Take care.