It's really confusing. USB-C is a physical connector that can carry the USB protocol, as well as power over the USB-PD standard, PCIe over the Thunderbolt protocol, DisplayPort over Alt-mode, and probably more that I'm not thinking of. The versions of USB that you're seeing are just for speed of file transfer, nothing else, except USB4 which adds support for USB-PD, Thunderbolt, DisplayPort, and everything else. The ports on your laptop are all Thunderbolt, which is equivalent to USB4.
If all you want is power, you need the cable to support USB-PD, which every cable that I know of does. Any cable should work. However, if you want to charge at more than 65W (which you probably don't because your laptop is small), you'll need a cable with an "e-marker" chip—just get a cable that is rated for whatever wattage you need.
If you need to transfer lots of data (which it doesn't sound like you do), you'll probably want something like USB3.1 (also known as USB3.2 Gen 2 and USB3 10Gbps) or USB3.2 Gen 2x2 (USB3 20Gbps) cable (yes, their naming scheme is horrible). If not, USB3.0 (also known as USB3.2 Gen 1 and USB3 5Gbps) or even USB2.0 should be fine.
To summarize, almost anything will work for your needs, but anything extra would require you to buy a cable that has explicit support. To make it easier for you, it looks like https://www.amazon.com/dp/B07T19KQYF has support for everything that you might need and much more: full power delivery up to 100W, more than twice what you need; 20Gbps Thunderbolt data transfer and 10Gbps (USB3.2 Gen 2) USB data transfer, many times more than you need; and displays connected to it, even though you don't need it. I'm not sure if it has full Thunderbolt PCIe support, but that shouldn't matter to you, and the price is pretty good.
Why do you say it's "not really" immutable? It is immutable with an A/B partitioning system using ABRoot.