Now when I click I get the animated "..." progress indicator, but that never stops, even after 4 minutes:

As I speak that indicator is still being shown...
Note: that API commands sent via the Sesame HomeBridge plugin do sometimes go through, but it is hit or miss, can be 30+ seconds later, and often the status reported back is "lock not responding."
Connecting to the Access Point from outside the home via the iOS app sometimes works but often it shows "Sesame Found" but then gets stuck on "Connecting..." So there is definitely something up with the server or the access point...