Is there a way to find a lost Apple Watch at home without Find My App?

Sorry, but the last location fo your device can only be displayed for 7 days, after that it can only be located, if it connects to a network again:

Find your lost Apple device or AirTag with Find My - Apple Support

The only other way to locate your Apple Watch, would be manually searching for it.

Apple can not locate your device, only you can:

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Locate your device

In Find Devices on iCloud.com, select the device in the All Devices list on the left.

• If the device can be located: it appears on the map so you can see where it is.

• If the device cannot be located: You see Offline below the device’s name. The last known location is displayed for up to 24 hours. Select “Notify me when found” to get an email when it is online again.

• If you turned on the Find My network, you can use the Find My app on any device that is signed in with the same Apple ID to see your device’s location, even if it is offline. The last known location is stored for up to seven days. See the Apple Support article Find your lost Apple device or AirTag with Find My.

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copied from: Locate a device in Find Devices on iCloud.com - Apple Support

I guess, the technical effort and the costs to track all existing Apple devices would be enormous.

Plus, I would be concerned about the missing privacy of this personal data.

Which might be one of the the reasons, why Apple does not keep those recored for a longer period of time.