Most new, digital thermostats include a function that prohibits the a/c compressor from restarting for 5 minutes from when it last turned off, as the required temperature has then been attained, to prevent the system compressor from “over-cycling” and burning out too quickly and needing expensive repair/replacement…
I don’t have central AC in my house, but when I looked into that feature when replacing the thermostat for our RV heat/AC, I found that the compressor restart delay was part of the AC control board, instead of the thermostat. The fan will come on, but the compressor will be delayed. That info was supposedly the same for home AC as well.
It has this feature along with compressor protection.
Minimum Run Time
Extend the life of your HVAC system. Use the Minimum Run Time feature to set the minimum amount of time the system should run for after you’ve turned it on, even if it’s been manually turned off.
Heat pump systems have a defrost board at the outdoor unit with it’s own time delay.
I just listened to my A/C unit turn on - run for less than 1 min and then turn off. ~30 sec later, it turned on again and the compressor did not sound happy! Just finished looking for the advanced settings (Android app v2.33.0 161) and I did not see anything related to compressor protection. The temperature differential was set to 1F so I changed that to 2F hoping that might help stop short-cycling.