I actually built the frame from crappy construction 2x4s milled down to 3/4 x 3 because this is mostly a proof of concept and learning project.

You can use a table saw to do a decent approximation of what a planer or a jointer does by fixing the work pice to a sled. This worked kind of poorly for me, but that was my fault, and next time I'll do a better job. I spend a lot of time sanding out saw marks and never got a great result.

Tamar uses a planer in this video for the first side, but I think you can see how you could do it just with a table saw, for small pieces.

https://www.youtube.com/watch?v=AWOB-WIDkOs

You could do maybe 3.5 inch pieces max on the table saw (blade height). Surely the front face of the drawer is bigger than that?

That's exactly right. Only works for small pieces. My drawer is a pull-out tray type drawer that I am adding to a big cabinet.