Hi Pete, may I ask you how you do this step? I feel so dumb as I haven't yet managed to figure out how to migrate existing accounts in my MS Authenticator app. I don't see any QR code for any existing accounts there.
Most of the authenticator apps I have looked at had very minimal features for even migrating to a new device with the same app, to say nothing of extracting the info in order to put it into something else. So if Microsoft Authenticator doesn't appear to have any way of doing that, or a way to get it to display the QR Codes so you can repurpose them, you may be forced to do it all over again from scratch.
I avoided most of this because I am meticulous about keeping all the details for every account I use, so i have a folder for each one and each folder contains a text file with my sign-in credentials, the QR Code, and possibly some addioinal recovery keys or backup codes. I keep all of this on an ENCRYPTED disk image so i don't have to worry about storing too much sensitive information since there's just no way someone could ever open it. So, if I was in your position, I would already have all of this info set aside and could just use it to set them up in a new app, or in iOS 15 ot macOS 12. Not a BATCH solution, I grant you, but it really didn't take much time.
The upside to Apple's implementation is that it's all connected to iCloud Keychain so all your devices are kept synchronized, so you aren't at the mercy of accidentally somehow not having access to the device its all stored on. Also, it's very easy to export and importt all of this info via .csv text files if necessary.
Hope this helps.
-Pete