Spending an evening sipping hot chocolate and watching utubes is how most choose to become finish carpenters if they can't spare time for ojt.

You need some good pro help this is so not to code I am not sure what would be involved the pics do not tell the whole story for sure .

24 inches seems quite narrow already so maybe you can remove the sheetrock attached to the wood-shims and the shims and glue sheetrock directly to the concrete. This should line up with your post above so you can then run the sheetrock all the way to the ceiling.

To finish the sides you can either sheetrock around the notch or furr out the post to the same level as the foundation for a cleaner look then install corner bead, mud and paint. It will be a lot more finished looking and then you can put in a little bit wider treads on bottom two steps.

I think that info is good about rmoving the stud and gluing drywall to the concrete but it depends on how much moisture gets into that concrete I did it in my last house no issues for 18 yrs but no moisture in the concrete

Id love to make the steps wider, and Im sure many parts of this old house are not to code. Who doesn't love old house renovations and the mysteries behind walls. Removing the stud is an option, with vapor barrier to help any moisture- we are in a very dry area so that helps.

Maybe adding a landing at that point? And sheet rock that corner to remove the negative space?

The 1970's should have a modern basement and codes that match today's standards. Nothing here is grandfathered in as some people like to use that as a crutch. Things appear to have been DIYed to the nth degree.

I would personally pause and evaluate goals, current and future. Investigate to understand how the stair is 12" skinnier, and why the guardrail is not typical. Maybe what changed on the floor above. Maybe why the side wall was thickened/furred out.

I would not just accept it and build on top of bad, it always is eventually realized a mistake was made and you will be in a worse off situation.

Instead of literally hitting a wall by trying to widen on the right side, consider how to widen some of the steps on the left side. You have what looks to be railing and open floor. Can the railing be removed, some of the steps widened near the bottom and the railing modified? You may not even need or want a rail for the bottom two or three steps.

You can learn a lot by getting copies of permits for the house from city hall. If the changes to the staircase were done to code way back when, it may give you some insight into how to handle the changes you want this time around.

If it were me, I'd just drywall around the notch and call it a day.

Ironic how no one on this forum would accept a 24" wide door to a bedroom, yet are perfectly fine with a 24" wide stair to basement, which constricts to interpolated about 20" the last 2 steps.

Again, a typical 1970s house is on par in it's bones with a 2020s house, this isn't a 1920 cellar.

Pull the drywall and blocking stud, grind the concrete wall to flat, and paint it. You just gained 2".