Linux

For something like a USB-C to C or USB-C to A, If you have something like an external M.2 SSD with a USB C connector and a fast enough port on your PC, you could see how fast a large file transfers. For USB C to C, most things I think should be USB 3.0 or higher, and you can tell whether some USB As are USB 2.X or USB 3.X by looking down the end and seeing whether it has that smaller fifth pin in the back. The color of the plastic tab in the USB can sometimes be an indicator, albeit an unreliable one as manufacturers are always screwing around with the colors. Blue usually means USB 3.X, black sometimes means USB 2.X, and white sometimes means USB 1.X. Any other color like orange is more likely to mean USB 3 than not, but not necessarily.

For USB A to Micro USB, I am fairly certain those will be USB 2.X. I am not aware of any micro USB device which operated at USB 3.X speeds. The only thing to watch out for are cheap cables with only power and ground populated and no data lines. But the easy way to test that is to just see whether a device is detected and identified at all by your PC through the cable, as that means the data lines are populated.

HDMI, I'm less sure, but if you have a high resolution/refresh rate monitor, you could try connecting it between the PC and the monitor and see what resolution/refresh rate options are listed, or seeing if there are visual artifacts or noise at the highest settings.