The finished products, I made one left-handed to be inclusive.

Here is the pile of scrap I started with.  I think I ended up using 4-5 of the 2x4 scraps, because the pile was about half this size after I was done.

I squared everything up on the table saw and cut to ~3/4" thick pieces for the desk/seat/upright pieces and ~1/2" for the other pieces.

These strips were in the best shape so I glued them up to make the desk & seat.  I cut the shape of those out mostly with a jigsaw and then rounded over on the router table.

Here are the pieces that will make up the chair/desk support.

Tenoned on the table saw.

Mortised in the mortise machine.

Everything seems to fit, I rounded over the pieces that would not be supporting the seat or the desk.

Glue up. I painted the chair/supports white 2-3 coats of whatever white paint I had handy.  The seat & desk got 4 coats of shellac.