I've always had problems using Disk Utility to Restore a bootable macOS drive. I will only use Carbon Copy Cloner (CCC) to clone a macOS boot drive (you can clone the drive you are booted from as long as you are not doing any other work at the time). To make a bootable clone of Big Sur or Monterey you need to right-click or control-click on the destination without CCC and select the "Legacy" option, otherwise only the data is copied.
I believe the last macOS update broke the ability of CCC to clone a bootable macOS drive (at least with Monterey, not sure about Big Sur). I don't know if there is a patch for CCC or a work around since Apple told the CCC developer a while back that cloning a boot drive would not work at some point (everyone assumed that would be the next major OS version upgrade and not a minor point release update patch). I believe the CCC developer is suggesting to perform a clean install of macOS and create a new macOS user account, then use CCC to copy your data. I'm sure Bombich, the developer of CCC, has information on his site about the issue. You could just as easily perform a clean install to the external drive and use Setup Assistant on the first boot of the clean install to migrate from the internal SSD.
SuperDuper is another cloning app which is well respected. I don't use it, so I don't know exactly how it works.