In general, erasing and installing the OS makes no sense in Monterey. The OS is sealed, and as such, it cannot be any different than it was when installed, or it basically won't boot. I can't see how this is going to help your issue.
But, yes, during FIRST BOOT of a fresh/erase install of the OS it will prompt to 'restore', and you can select your SuperDuper backup at that point (either a bootable backup or a "data volume only" backup).
But my recommendation is to diagnose the Time Machine problem without wiping the system - I can't see how that would help. (However, apart from suggesting you format as APFS and try selecting it, I'm not sure what to recommend, since - as you know - I didn't write Time Machine and haven't had this problem.)
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--Dave Nanian
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