Why not just hang some buy some dark drapery panels, thread them on dowels, and hang via chain from the floor joists?
You could make some acoustical panels and hang them behind the drapery panels too. Hang the screen via chain.
Hit the end of the roll carpet area, for inexpensive carpet remnants. Or you could do a DIY acoustically transparent screen.
And the wall could be screwed together and held in place by a couple of screws into the floor joists, plus a couple of dabs of
silicone under the foot plate.
Minimal work to return the basement to it's original condition.