Setting up New MBP with Time Machine

If the new computer is going to be the Apple Silicon M1 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

Some have had success and other have been left with a mess when Migrating everything.

1 - Issues that may exist on the computer where the Time Machine Backup was created will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

2 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

As one ( you ) is moving from an Apple Silicon M1 to a newer Apple Silicon M1 - most if not all Application should work fine with exception of problematic Applications.

Then a Clean Installation of the problematic would be suggested.

Not really, aside from Empty Space on the New M1 Machine versus the Old M1 Computer.

Just a foot note - neither of the two suggestions provided, are the Absolute Right Answer.

The " comfort level " of the User ( you ), confidence in either of the two methods suggested, is more important than anything else.

Thereafter - Do you have a Rescue Plan In-Place. This comprises having 3 Backups using 2 methods and 1 Off Site incase of Theft, Loss or Natural Disasters. A Time Machine Backup  is very useful.

For addition purposes - two Tested Clones each to separate external drives. This is insurance incase . At least one Tested Clone and / or Time Machine Backup should be Off - Site

Does my CCC backup have to be bootable for me to restore data from it?

Is your old Mac really an M1. If so it cannot be very old. That being said I always use TM to migrate all at the initial setup on my new Mac. Since you are going from Big Sur to Monterey the transfer should be very smooth. I see no reason for you to exclude anything. You may have to reauthorize an app or two. I recently did this and no issues at all.