Electrical – Does open stairs between basement and main living cost extra electricity bill

The lack of insulation on the ducts in the floor is of no concern as the floor is in the conditioned space (ie, the area around the ducts is supposed to be cooled.) If the ducts were in the attic that would be a BIG deal.

The very low insulation in the attic seems like both a contributing problem, and the most easily solved one. Either rent a blower and buy some insulation or hire a company to do the whole job and insulate the attic a lot better. Read up carefully before deciding to try the "free blower with 10 bags" at the big box stores. 12-16" is a good number to shoot for, where possible, but you may (probably will) need to baffle for your roof vents at the edges to go that high.

Better windows will HELP but they are more costly and complex to do and involve a smaller area (thus, less overall contribution to the problem) than the attic does - grab the low-hanging fruit first.

Improving attic ventilation along with or before the added insulation will help with both cooling and with ice dams by keeping the attic space above the insulation closer to outside air temperature.

If you find that your system is still undersized, adding a couple of higher SEER mini-split heat/cool systems (on the upper floor, perhaps one at each end of the hallway) might be a better approach than replacing the whole thing. Might not, as well, but should at least be considered, IMHO.

Same sort of basement entry here in Seattle. Intermittent flooding and the hassle of sweeping wet leaves out of the stairwell for too many years. I love my current solution.
A friend drilled support-heavy screws into the concrete foundation. We cut 3 pieces of heavy duty plywood to cover the space and fit around the bases of the railing at the top. One end of the wood rests on the screw-supports. The other end rests on the concrete on the other side of the stairwell. (3 pieces because they are heavy - so the dog would not crash through if he walked on them.) Rain rotted my first try, so I bought sheets of that rippled Fiberglas roofing type material and cut them to size.
If you get the picture, you’ll be able to figure out how to keep water from getting into the wood through the seams in the Fiberglas. The stairwell stays dry all winter. I can store lawn chairs and such down there. The cat can go there and sleep. I can still access the stairwell if I need to get out fast by crawling out or lifting the plywood from below. If you don’t have animals, you might be able to use just the Fiberglas sheets. PS make sure this cover slants so the rain runs off. My screw supports are just a little under the siding.