Example below,
Is this popup style now available standard in iOS? (Perhaps as one of the huge number of variations of the new 'popup style buttons'?)
I know that some people on here are clever enough to inspect apps and see what the classes are; I can't.
Is this a standard now-available interface element, or is it just custom programming?
It's a "full time job" keeping track of what's available in UIKit and I do not know the answer in this case.
It's Pop-Up Button made with UIMenu
(main starting class) and is available on iOS 13+ (since your question is about iOS).
An intro on WWDC 21: Meet the UIKit Button System (at ~12 minutes)