If you are installing a virgin OS on the drive (meaning that the drive was empty), Setup Assistant (equivalent to Migration Assistant) launches immediately when the drive boots. At that point, select either the clone or Time Machine and let it import everything. Don't set up any accounts before you do this. Setup Assistant will bring everything over to the new system and it will look just like the one being imported.

Read Set up your new Mac and If the Mac setup assistant says that your user account already exists, just in case. It's much easier to use SU than to set up new accounts and then use MA.

Jon

macOS 11.7.10, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365