IMHO, there has been sufficient advise offered, from more than one Contributor, for the User ( you ) to make an informed and educated choice what the next course of action is required.
That said, perhaps the user requires to focus more on the needs that the wants aspect of this process.
The below may or may no work and does increase the risk of Pollution of the New Computer.
The User will Need to spend some Time to perform these actions in a Detailed / Tedious manner plus the knowledge / skill-sets to execute this suggestion.
Evaluate the Older Computer and determine exactly would Third Party Software, Extension, Drivers and Personal Data the user Does Not what Migrated to the New M1 Computer.
Remove the above outline above item making certain all elements of the above are not longer on the Older Computer.
This should, in theory, mean what is Now on the Older Computer is what you want Migrated to the New M1 Computer - right ?
Get a new or re-purposed External Drive and create a New Time Machine Backup one the above has been accomplished.
This New Time Machine Back Drive can be used to migrate to the New Computer and fulfill the " PICK AND CHOOSE " requirements the user has outline in earlier posting.