What, if anything, has changed regarding retrieving an older version of an iOS app from a local backup?
iTunes 12.6.5.3 was the last version that had the ability to download apps.
On September 12, 2018 Apple released iTunes 12.7.0.166 which removed the built-in App Store browser and thus the supported ability to store downloaded copies of apps on the machine that iTunes is running on.
https://en.wikipedia.org/wiki/History_of_iTunes
See also the article (and comments for) Apple Releases iTunes 12.7 With Major Changes, Including No Built-In App Store
If you want to do this today, you need to archive the older version of said app BEFORE you want to restore it. You can do this with a tool like iMazing, that allows you to maintain a local library of apps that are installed on an iOS device.
Caveat: You must download the app to the local library while it is still available from the MAS. There is no way to retrieve it from the iOS device.