When you say system drive this will also have your efi system partition (usually FAT-formated as that’s the only standard all UEFI implementations support), maybe also a swap partition (if not using a swap file instead) etc… so it’s not just copiying the btrfs partition your system sits on.
Yes clonezilla will keep the same UUID when cloning (and I assume your fstab properly uses UUIDs to identify drivees). In fact clonezilla uses different tools depending on filesystem and data… on the lowest level (so for example on unlocked encrypted data it can’t handle otherwise) clonezilla is really just using dd to clone everything. So cloning your disk with clonezilla, then later expanding the btrfs partition to use up the free space works is an option
But on the other hand just creating a few new partitions, then copying all data might be faster. And editing /etc/fstab with the new UUIDs while keeping everything else is no rocket science either.
The best thing: Just pick a method and do it. It’s not like you can screw up it up as long if your are not stupid and accidently clone your empty new drive to your old one instead…