I never had any problem connecting mobile devices, IoT devices and PCs to my Cisco wireless access points that hang off my Vigor 2927 router (with fimware 4.4.3.1). But recently I had great difficulty connecting some additional home infrastructure devices: a Ring Stick Up camera and a Rheem water heater controller. The Ring installation app suggested that I restart my router, whch I thought strange. However in both cases I was able to easily register the appliances immediately after rebooting the Vigor 2927. Does anyone have any suggestions for why this might happen?

There could have been lots of reasons.

Also, some users on here, me including, have previously reported problems with WiFi on some DrayTek devices.

It's not clear whether you were trying to connect the new devices to your Cisco access points or directly to your router. Perhaps clarifying that would assist someone with knowledge of the Cisco's to help?

Thanks and the added devices both were connecting using the Cisco WiFi Access Points. But note that the devices did not report issues with connecting to or authenticating their WiFi connections and I did not restart the access points, I only needed to reboot the 2927 router in order for the devices to register to their respective mothers in the cloud.