What is the least expensive way to put up new bedroom walls?

Drywall is cheaper than plywood.

2 x 4 studs are cheap, you’ll need to put in a soul plate, and studs at 16 inches on center with the top plate screwed into the ceiling joists.

Scraps of drywall, are going to be a lot of work to steam them where there is no natural seaming spot. You will notice that drywall has beveled edges onto sides only. Those are made for using the drywall mud and tape.

#1 thing to do is Planning:

In order for your work to be legal, when you sell the house later,

all bedrooms must have a closet and all bedrooms must have an egress window of certain minimum size to get out if a fire happens.

You can check on line what generation of the national building code (IRC) that your local city uses, which will determine the size of the egress window.

The egress window must also not be any higher than 40 to 44 inches above the finish floor., Once again depending on your local jurisdiction agencies.

Depending on what state you live in, there will be additional requirements like minimum natural daylight and a minimum natural ventilation, they are percentages of the total room square footage.

If you choose to build an illegal bedroom, then that is your choice, but when the house sells, in the future, you can be forced to rip it all out, for the buyers.

I would opt for using leftover drywall as long as thickness matches. Already paid for! Tape, mud and sand. Paint. If you want a quick feature wall, paint it a different color or use textured paintable wall paper and paint that. Done deal.