Using an icloud backup will result in the newest version being loaded, so I think I need to make an IPA file of the app and use configurator to load it onto my new phone. However, I need an IPA of the current version I have, not the updated version. Is there a way to do this?
This can be done from Configurator 2 if and only if you already have the .ipa file.
iTunes used to sync .ipa files back from the phone as part of the backup strategy. This practise stopped some years ago & has since relied entirely on OTA downloads of current versions from the App Store.
It may be possible to use the older & now unsupported last version of iTunes that allowed this, to extract an .ipa from the current phone, which you could then re-sync to a newer phone… assuming it will run on the newer phone.
The link to the last version of this 12.6.x.x is here - Apple KB: Deploy apps in a business environment with iTunes however it appears it will not run in later macOS versions without some effort. See MacRumors: iTunes 188.8.131.52 on MacOS Catalina and also apparently will still work for an iPhone 8, but not an 11 - Reddit: Does iTunes 184.108.40.206 work with iOS 14?
All of this does imply it might be a tougher job than it once was. I cannot test any of this empirically, I'm afraid.
As a long shot, you may have the .ipa buried deep within Time Machine, if it goes back far enough. This was actually how I achieved a similar task a few years ago.
@Tetsujin is correct, mostly. In the spirit of completeness:
There are 3rd party iOS backup programs that will do this. I got iMazing as part of an app bundle and found it to be my most useful app. Note that I hold no interest in the company that develops the app, just a happy user.
iMazing (I believe iExplore as well) will back up the.ipa files to your Mac. Once they are on your Mac you can then restore them to another iOS device.
Obviously this will take up a fair bit more disk space on your Mac as you are storing the iOS apps there as well. Also I think it has a free trial period, so that you could verify that it does what you need it to do before committing your hard earned $$.