Just out of curiosity I did check

Kroger’s Privacy Policy

in select Texas stores we may collect biometric information such as a facial recognition data, when you enter our stores for security purposes, to protect the health and safety of our customers and associates, and to prevent, investigate, and prosecute shoplifting, fraud, and other criminal activities. We provide notice at the point of entry in locations where we collect biometric information.

So, only in Texas and theyre supposedly not trying to hide it ? at least for facial recognition. ALPR isn’t specifically mentioned in Kroger’s privacy policy, although this line implies it’s not entirely off the table

Sensory data such as CCTV recordings from our facilities or premises or photos. Some of our cameras may capture license plate data for security purposes, to protect the health and safety of our customers and associates, and to prevent, investigate, and prosecute shoplifting, fraud, and other criminal activities. We may record your voice when you contact our customer service centers.