I've checked the Date/Time settings on my phone and it was fine. It showed "Set Automatically" and displayed the correct time zone. I did turn the setting off/on and restarted the phone. The setting stayed, but it did not make a difference with the Find My app.
To my knowledge I do not have a family sharing group setup. I just sent requests to each family member individually and it has worked great this way for at least two years.
The alert appears almost instantly when you try to open the Find My app. The alert reads "Share My Location Unavailable. Unable To Connect To Server. Please Try Again Later". It only has problems with the "People" part of the app. I also have an iPad and AirPods and the app never has problems locating those "Devices" even it the devices are taken to a new location (such as my work). It also locates "Me" with no problem.