Commuting gear is whatever you use for commuting. If it works, it works. And having "commuter" on the label is no guarantee that it'll work for you.
I'd avoid anything particularly lightweight, as its possible to wear through the fabric by carrying stuff with defined corners like books or laptops.
Personally I'd also avoid backpacks for running, as they're usually designed to sit higher, almost on the shoulder blades.
While good for some things, this means you carry more weight on your arms when riding.
If you're on a budget, pick any backpack with a waist and chest strap that looks the right size. You can even get one from a thrift store or something. Try to find one that sits low on the back. Then buy a hi-viz, rain proof backpack cover.
https://www.amazon.com/gp/aw/d/B01N...7-c7d3-5b5e-a47e-56f1befc65d5&pf_rd_i=3400441
Something like this:
Although for commuting I do prefer to use a rack and pannier.
Gets rid of the sweaty patch on the back that backpacks tends to create.
For commuting it makes sense to use fenders anyhow, so there isn't much lost to the bike by adding a rack.