Update: I ended up having to do a factory reset. I am still going through re-pairing the devices I had connected before. I did the thermostat first. Both last night and this morning, it changed settings according to schedule.
Of all the devices, the thermostat was the only one not properly behaving that I know of. The other Z-Wave devices (siren, glass break detector, smoke/CO detector) could have been also not functioning properly but since those don't give any indication, I wouldn't have known. The response to my trouble ticket was that the Hubitat's database had become corrupted. I think this might have happened when a car took out a telephone pole near us and our power was out long enough that the UPS to which I had the Hubitat connected ran out of power so the Hubitat had a dirty shutdown. I tried a soft reset and restore from backup, but I suspect the backup was also corrupted. Thus, the factory reset and going through the process of re-pairing everything.
Once everything is connected again, I will be sure to make a backup and to label it this time so I won't delete it. I'll probably make a folder specifically to hold the backups so they won't be mixed in with other files. With this, I guess this issue can be marked as Solved.