For me, this problem only started occuring when I updated to macOS 10.15.1 last week. I never had this problem before on any prior major macOS versions with either my 2018 Mac mini or my mid-2011 iMac.
The problem occurred again last night. During the week, I finally figured out how to have Catalina show all my devices under "Locations" in "Finder".
Last night, one of the iPhones (a Xr) had a rotating circle icon to the right of the phone's icon, which indicated (to me, at least..) a hung process. Catalina greyed out the option to back up this particular iPhone, although Catalina still enabled the back up option on other devices (they didn't have the rotating "circle of death" next to them). As soon as I powered off the iPhone Xr and it dropped out of Finder's Locations, the Finder error message disappeared. I powered down the Mac mini without issue.
Does anyone know how to troubleshoot the spinning arrows next to an iPhone when it's under "Locations" in "Finder"?