The disk (eMMC) has many partitions, and only one is the root file system (rootfs). Clone is only of the rootfs. “rootfs” does include “/home” in the default layout. Most of the CUDA related content is only in “/usr/local”, and a clone does include this if you are just using eMMC (a clone contains everything in “/” of the rootfs partition, and of course being a tree structure, this means all subdirectories of that particular disk).
A clone is a great backup tool if you keep the raw clone (a clone will produce both a “raw” backup.img.raw, and also a “sparse” backup.img…only the raw file can be examined and manipulated, but both can be used for flash…sparse is a faster flash at the cost of not being useful for any other purpose).
Booting an entire system from an external drive has many details to be careful with. Copying only “/usr/local/” content to the extra drive, and then mounting at “/usr/local/”, is very simple/quick and you can afford to make mistakes.
You can do something similar with “/home/”, just like “/usr/local/”, but then you mount the external hard drive partition to “/home” instead of “/usr/local”. You could split your hard disk into two partitions, and mount one on each.
Two separate partitions can be a bit inflexible, but you could instead use a volume manager to use all space on the external disk, and then mount a “/home” and a “/usr/local” volume (a logical partition) instead of discrete partitions. Volumes can be changed dynamically (though not while being used…you have to take special steps to safely manipulate volumes) to split up how they share space, and new partitions can even be created with spare space. Basically a volume manager marks the disk as a “pool of space” instead of marking specific layouts.
Anything volume manager is standard across most Linux distributions (unless you are booting to that…for “/home” and “/usr/local”, this is not being booted to). See any of these (lots of documentation available on the internet):
https://ubuntu.com/search?q=lvm
https://www.ostechnix.com/linux-basics-lvm-logical-volume-manager-tutorial/
https://www.howtoforge.com/linux_lvm
https://www.digitalocean.com/community/tutorials/an-introduction-to-lvm-concepts-terminology-and-operations
Keep in mind that volume managers are not simple to resize (well, relative to just having partitions). You would need to learn things about this. In some cases actual partitions will be resizeable with tools like “gparted”.
Simpler tends to be better. Tools under “/usr/local” tend to be large, but will not necessarily change a lot. “/home” content can have projects and change a lot. Find out what you currently have for total content at each:
sudo du -h -s /home
sudo du -h -s /usr/local
Copying content from that onto an external drive would at minimum require that amount, and can free that much from the eMMC if you choose to do so. It is very important to know what it is you want to accomplish and what kind of flexibility you need.