AFAIK, the app is just the website in a webview.

This is the way. It's prudent to treat apps with skepticism, it's unfortunate it's come to this.

I study Apple's Privacy Nutrition Labels religiously every time I consider installing an app.

I like the ones with "Data Not Collected".

With Firefox, yes. I wouldn't fully trust other browsers to care about my privacy.

I think you need the app to use the delivery lockers (which I prefer over home delivery)