The site you linked is where I got my cleaver and I vouch for exactly what you’ve said. Though I haven’t seen an issue with my onions. I don’t oil the blade often but I do use it to chop meat (and thus their fats) once a week.
I’m pretty sure I got their #3 veggie cleaver, though I’m not really sure the difference between that and their carbon steel cleavers. Works fine for meat, but I don’t chop bones with it.
Got any tips on sharpening? I feel sloppy whenever I’m doing it and it seems like you take a pride in it, so if I could pick your brain on how to sharpen my cleavers better, I’d appreciate it!