In general going backwards in time is messy.
Depends a bit on what you mean by restore.
1. Finder copy:
Assuming you already have Big Sur running on the laptop, connect the Monterey TM disk. You can then use Big Sur Finder to navigate to the Monterey TM disk and drill down to the files or folders you want to restore. Then Copy them from the TM disk to somewhere on the Big Sur disk.
You should not attempt to copy anything from ~/Library to Big Sur's ~/Library.
If you attempt to copy any libraries (e.g. Photos), they will copy OK, but will be unreadable by the older Big Sur software. You would need to drill down inside the Photos Library to find the original photos and copy them. Probably better to make sure the Monterey photo library is synced to iCloud before you start and then connect Big Sur's Photo app to iCloud.
And, of course, different architectures (e.g. iMac is Apple silicon (M1) and laptop is Intel) will add complications but should be fine for copying documents, photos, etc.
But a) it is possible that you will only be able to access the most recent Monterey TM backup, and b) I would expect there to be missing files if your wife was using Optimised Storage (Documents and Desktop folders partially in iCloud) with Monterey.
2. Migration Assistant:
You will not be able to do a system restore using Migration Assistant because Monterey has software and settings that are newer than Big Sur. Big Sur does not know about changes in any future (post Big Sur) version of macOS.
I have to ask: why not update the laptop to Monterey?