IME things are not just processed under general merchant Square code, they are specific to the business. proof is that there are a lot of food trucks around where i work and most use Square to take CC, of the two i've been to in the last few weeks, both processed as dining when using my Chase Sapphire card and earned 2x points.

As for "selling pens and notepads out of my garage on the weekends as a hobby", there's no such thing. I don't know all the hoops to jump through but if you were to set up a Square account and somehow get it to code as office supply, well and good, you may earn your rewards. However, the government will expect you to report all those transactions as business income and will then tax you on your "sales", which would effectively negate any rewards earnings and probably cost you even more.

I doubt using Square lets people bypass income reporting to uncle sam.