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From this article: Set up an Apple Watch for a family member
"Note that some Apple Watch features depend on having a companion iPhone, and aren't available on an Apple Watch that you pair using Family Setup."
Also note, from: If your Apple Watch is lost or stolen
"Here's how it works
When you use Find My, your Apple Watch with GPS and cellular can use GPS and a trusted Wi-Fi or cellular connection to show you its approximate location. Apple Watch with GPS can use GPS and a trusted Wi-Fi connection."
Lastly, About privacy and Location Services in iOS and iPadOS
"How your device uses Location Services
With your permission, Location Services allows apps and websites (including Maps, Camera, Weather, and other apps) to use information from cellular1, Wi-Fi2, Global Positioning System (GPS)3 networks, and Bluetooth4 to determine your approximate location5.
Apps that can show your location on the screen, including Maps, show your current (approximate) location using a blue marker. In Maps, if your location can’t be determined precisely, you’ll see a blue circle around the marker. The size of the circle shows how precisely your location can be determined—the smaller the circle, the greater the precision. When Location Services is active, a black or white arrow icon appears in the status bar.
Maps, directions, and location-based apps depend on data services. These data services are subject to change and might not be available in all geographic areas, resulting in maps, directions, or location-based information that might be unavailable, inaccurate, or incomplete. Compare the information provided on the device to your surroundings and defer to posted signs to resolve any discrepancies.
Learn more about Location Services and privacy.
Improve GPS accuracy
GPS accuracy depends on the number of visible GPS satellites. Locating all visible satellites can take several minutes, with accuracy gradually increasing over time. To improve GPS accuracy:
- Make sure that you've set the date, time, and time zone correctly on the device in Settings > General > Date & Time. If possible, use Set Automatically.
Keep a clear view in several directions. Walls, vehicle roofs, tall buildings, mountains, and other obstructions can block line of sight to GPS satellites. When this happens, your device uses Wi-Fi or cellular networks to determine your position until the GPS satellites are visible again.
Crowd-sourced Wi-Fi and cellular Location Services
If Location Services is on, your device will periodically send the geo-tagged locations of nearby Wi-Fi hotspots and cell towers to Apple to augment Apple's crowd-sourced database of Wi-Fi hotspot and cell tower locations. If you're traveling (for example, in a car) and Location Services is on, a GPS-enabled iOS device will also periodically send GPS locations, travel speed, and barometric pressure information to Apple to be used for building up Apple's crowd-sourced road-traffic and indoor pressure databases. The crowd-sourced location data gathered by Apple is stored with encryption and doesn’t personally identify you."
Are you able to share the location of the watch and does it appear to be accurate or are the results the same?
Use this article as a guide: Find friends and share your location with Find My With that, is the watch currently on the wrist? If not, place it on the wrist and then test for location accuracy with Find My.
Regards.