I have the Eufy Battery Video Doorbell installed with a hard wired power connection.
Like another user reported here, motion detection from the doorbell is sometimes hit or miss. I have tried tightening the detection zone and have also tried removing the detection zone completely. Sensitivity is set at the highest level which intuition would say should catch more movement.
Persons entering and leaving the house are routinely captured on video, however there are sometimes cases where movement is missed for some reason. The main concerns is when packages are left by delivery folks and somehow the motion is not detected. Same with package pickups for outgoing packages. This is one of the top reasons for having a video doorbell and missing these events is troubling.