This script pulls the device counts from each site in a Jamf instance. This script currently does not handle finding devices not in a site, but that is something that would probably be useful to include.
Enter credentials for an account with Full Jamf Pro access. It just needs read access. Run the script to get a CSV file that has each site count with columns for Computers, Mobile Devices, and Apple TVs.
My instance was affected by a PI where there were stale records. Some site counts were off by as many as 20 computers. Jamf Support is able to resolve this, and they told me that this is a resolved PI, so once support cleans up the bad records there is no issue with them returning.