We can't tell what size of header is required because we can't see how much the stud wall is transferring to the floor/footers looking at your pictures. I'm assuming quite a bit since they doubled the floor truss and built a wall under one of them. A floor truss can normally go a fairly wide span unsupported, much wider (depending on engineering design) than dimensional lumber (2xs). I'd be more concerned about the load from above than the load of the stairs and stair landing. You could reengineer the landing by moving the 2x header up to the same height as the stair landing and sistering it to the landing. But to do this, you'd have to do it on both sides of the stair landing since the beam under the right side of the landing would need replaced on the other side as well. That would give you even more headroom for your access. Without getting an engineer to review and approve I would err on the side of over-engineering.
On my basement project thread I show an opening I put in for a new exterior door. When my plans came back they said I might need an engineer to approve depending on what the inspector says after the fact. The engineer was going to cost me much more than the cost of lumber, even at the inflated costs during the early COVID days. Due to several factors, I was installing a new 2x4 wall in addition to the 2x4 on 12' centers exterior wall built originally. When I opened the wall for the door, I added a double 2x12 header at the ceiling to hold up my breakfast nook. I then added a double 2x10 on the door opening. I had more than enough structure there that the building inspector was fine with my opening. Minus the cost of the lumber I saved over a grand.
Basement Project thread