How to build a wall under duct work
Possible options I see:

1 - Take the duct down temporarily or as needed.

2 - Build a flat wall in front of the duct, top plate to the left of the gas line &amp; that wire, to then do closets under the duct.

3 - Do an open four or square four (not this pointy 4) without the top right back leg &amp; of course a double long bottom leg.

I favor #3 &amp; it should be plenty stable enough, good place for the TV or a bar. Use Fir studs instead of the cheap pine studs, much stiffer. You can also double the top plate for the left turn &amp; double the front for the up-turn around the duct. I see the far wall that will also help. And, just insulate the face of the duct behind your wall.

If building-down the ceiling then I'd do that first, so you know if you're coming down enough &amp; if anything has to be moved, but it doesn't really matter if you can measure.