How To Recover Specific Items When MacBookPro Won't Boot
I would recommend a different approach to avoid unforseen problems and make it more predictable:
Install macOS on the external disk and boot from it. Mount the internal disk and copy files over manually to a 3rd location - either a separate APFS volume on the external disk or a 3rd external disk. Once you've copied and verified all files, wipe and restore the backup on the internal disk.