The BT dongles arrived, I inserted one and rebooted, and it didn't change anything. That wouldn't have helped anyway, because they're BT 4.0. And it was a radio I needed to replace originally, because one of my devices required BT 5.
Now I'll keep using my non-BT mouse and keyboard until I see if Friday's update fixes anything. Still considering getting a newer Latitude if not. A newer one with lots of current features (camera, 16GB of DDR4 RAM, etc) can be had for less than $500 (renewed).
Maybe I can re-purpose this laptop sometime for an application that doesn't need BT.
Thanks again, both of you, for trying so hard to help, but I now know it would probably take a new motherboard to fix the BT problem, and that would probably cost more than a renewed laptop.