Migration of files into bootable installer?

A bootable installer is just that: an installer that is bootable for installing the system on the internal drive. It's not a bootable clone where you also have your user data files.

You can create a bootable clone on an external SSD with Carbon Copy Cloner. However, getting the M1 to boot from it is very difficult as James has already discussed. It can be done but you'll have to due your due diligence and find out how to do it. I don't have an M1 so have no experience with it. I have cloned many times with an Intel iMac.

How to use Carbon Copy Cloner to clone to the EHD is described here.

First of all, a bootable flash drive installation of macOS can be rather difficult to get working on Apple Silicon based Macs (M1 / M2) and Intel w/T2 Security Chip Mac's. You have to be super careful or you'll have problems. There's firmware settings to allow USB boot but also secure boot considerations. The biggest is with Apple Silicon not being able to boot an external drive if the internal disk hidden partitions are deleted.

If this is an Intel Mac without a T2 security chip then booting from a flash installer image will work very well in most any scenario.

You backup your data using an external USB drive by enabling Time Machine and waiting for the first full backup to occur. There's also 3rd party backup software such as Carbon Copy Cloner and SuperDuper that can clone the internal disk to an external disk.

To restore the data, there is an option during installation to restore from backup, you would point the installer to the Time Machine or 3rd party clone and it can restore your data after macOS is installed automatically. Or you can run the Migration Assistant after installing macOS.