On a quick check a 90x90x3.6mm hot-finished SHS (square hollow section)
Grade S355 (Grade 43) steel would do the job and weighs only 9.6kg/m.

P.S. I bet it is much easier to weld trimmer joists into the landing space,
too, even if the wall thickness might need beefing up from the stairs point
load and the missing joist.

Christian.