DIAGNOSIS That spinning blue circle is a boot loop. It's trying to start up, failing, and restarting. This is almost exclusively caused by corrupted firmware or a failed internal memory component during an update.
FIX You need to force a hard reset and a fresh firmware pull. Press and hold the orange setup button on the front of the device for 20 seconds. Release it. The light will spin and it will reboot. This can take up to 5 minutes. Leave it completely alone during this time. It will download a fresh copy of the OS from Ring's servers.
IF THAT DIDN'T WORK If the boot loop continues after the 20-second reset, the internal battery might be so depleted it can't sustain the boot process even when hardwired. Remove the Quick Release battery pack and charge it fully via USB-C inside your house. Then reinsert it while the doorbell is still connected to wires.
HEADS UP During this process, the device is vulnerable to power fluctuations. If you're hardwired, do NOT disconnect the wires while it's booting. If you're on battery-only, make sure it's fully charged before starting the reset.