This used to be possible up to iTunes 12.6
Individual .ipa files for each app were stored on the user's local computer & could be restored to a new device [assuming they were capable of running on it].
Since 12.7, iTunes no longer keeps copies of .ipa files & after a new device install, apps are downloaded direct from the App Store - these will always be latest versions.
Apple did keep a special corporate version of iTunes available - currently 12.6.5 - via this link; Deploy apps in a business environment with iTunes but it requires you already have the .ipa files on your computer, or can pull them from the old device. I haven't tried this as a working method in a long time so can't quite recall the precise steps needed.
It also will not run under Mojave, so is quite a limited resource.