Migrating data to new laptop

restoring from a Time Machine backup, and using the Migration Assistant app

Those two are essentially the same thing, now. With the changes to the sealed System Volume, you no longer "restore" as the terminology was used. You Reinstall the OS and then Migrate your Data.

Downloading from iCloud: Are you using Desktop & Documents in iCloud Drive? If so, just sign into the iCloud account with the same AppleID and enable Desktop & Documents for that Mac (and likely Optimize storage).

If not using D&D, then I'm not sure the point of downloading the data unless you need to use it.

If there is enough space, migrate the user and settings from the old backup. I'd use a USB or Thunderbolt connection, if possible.

I have done something similar, but before I started migration, I had to make sure that they're on the same operating system, Monterey. From there, I configure the new Mac and used Migration Assistant and connected both via a Thunderbolt cable - this is fastest, IMHO.

Good luck.

Why don't you spend $50-$100 and buy a USB external drive? Then Time Machine a backup which can be used to restore to the new computer. That way you'll have a copy in case something crashes.

My choice for a number of transfers was a TimeMachine backup attached directly to the Mac with a simple USB cable.

Depending on the Mac model and year that may mean USB-A (normally referred to as "USB") or that cable with a USB-C to USB-A adapter. Apple sells a good adapter.