With my experience as of June 2021, you MUST have a cloud subscription to see your recordings with the App. You can pull the USB to see the recordings on a PC. From what I read in the 1-star Amazon reviews, apparently there was a software / policy change in April or May that effectively eliminated the usability of the Local Storage.
Conveniently for Amazon, they supply a 30 day free trial to the cloud with the purchase of a Blink Outdoor system. By the time you realize the Local Storage does not work as advertised and mentioned in reviews from 2020, your return window has closed. With a couple of long calls to Amazon customer service, I received a partial refund.
Look up the recent 1-star reviews. Look for several with “Bait and Switch” in the titles.