Yes, barrel switches should ideally be reported as "Barrel Switch" and "Secondary Barrel Switch". I have a Huion tablet[-1] that reports the second barrel switch as Eraser. The secondary barrel switch was not in HID originally[0], and I guess some devices were designed to follow an earlier spec -- that, or avoiding Wacom patents.

[-1] I don't remember if it's also a uclogic controller?

[0] https://www.usb.org/sites/default/files/hutrr46e.txt