If, tiles are parallel to the front wall (door), leave it alone. The staircase itself is tricky. The only adjustment you can make is at the top, where the top riser and nosing is located. You would shim and correct the angle there, then rebuild your staircase. Of course, the nosing may not be parallel to your wall afterwards. Framers screwed up somewhere.

A mat at the bottom of the stairs will break up the tile pattern and make the angled cut tiles.

I had that in a mudroom and it went unnoticed. A rug breaking up the visual pattern of tile is enough to mask the issue.

If the stair is at an angle, is the handrail wall is at an angle too (parallel to the load bearing wall)? Is the upper floor framing parallel to the front wall (I see the wood floor at the top tread looks angled) - would rotating the stair fix both tile and upper wood? Or, are the stair treads cut as a trapezoid shape (e.g. 34" long at top tread, 36" long at bottom tread)? is there another 1/2 flight down on the other side of the handrail wall?

So if the stair is inherently square as a unit in and of itself, it would be easier to rebuild the handrail wall and rotate the stair as a unit to align perpendicular to the front wall. Then fur out the load bearing wall perpendicular to the front wall too, instead of dealing with angled millwork.