Back-up migration

This article from Apple on Restoring files from a Time Machine Backup

refer below

Restore items backed up with Time Machine on Mac - Apple Support (CA)

From your above description, it looks like the computer has been booted into Recovery Mode for the Apple Silicon Computer

refer below

Use macOS Recovery on a Mac with Apple silicon

Excerpt from above link

• " Time Machine System Restore: Restore your data from a Time Machine backup. In the Recovery app, select Restore from Time Machine, then click Continue. To return to the Recovery app, choose Time Machine System Restore > Quit Time Machine System Restore. See Use Time Machine to restore your system. "

FWIW, unless your system install is corrupt there is no reason to reinstall macOS on a silicon Mac.

See: Erase your Mac and reset it to factory settings - Apple Support

Once done you can migrate your user data from Time Machine.

Follow on to previous reply.

Restoring individual files from a TM Backup does not require booting into Recovery Mode

Restoring your User Data to a previous period in time does required Booting into Recovery Mode

Notation on the latter of the two above statements

Time Machine Backup does backup only the User Data Volume on this computer.

Time Machine Backup does not contain a full and working copy of the Operating System

VeryVeryCheesedOff wrote:

Thanks for the directions. I have a silicon M1, and I have stored the data on a new hard drive, The problem is it does not seem to recognise that it is a hard disk, and insists that instead of simply restoring the data that for some unknown reason I should use migration as if it is from a different system.

Do you want to restore the data to your Mac? If so, then you use Migration Assistant, preferably in the Setup Assistant. If you already created a user with the same name as the data you want to restore, you will run into problems.

Just so you understand, there is no mass data restore function from Time Machine. You must migrate the data from the backup.

The sealed system volume (the operating system) cannot be reliably backed up and restored.

You must reinstall the OS, then migrate your data from the point in time you wish.

Welcome but it seems your question has already been answered with " Best Answer " designation