Trying to smooth out a circle cut out - I am stumped!

I am hoping someone could offer me some advice - I have created this spiral staircase design and want it to appear through a hole within the space (will attach an image to show what I mean) I have modelled this cut out, finished the stairs but I am not satisfied with the smoothness of the cut out. I do not want to remodel the cut out as it took a while to get the positioning and angle correct. I have tried smoothing the edges but this does not give me the effect I want. The model is currently in a group at the moment.

Smoothing the geometry will not change the number of segments in the circular hole.
Because you have incorporated the circle in other geometry it is no longer possible to change its segment count.
I suggest you do the following…
Ensure there’s something to be used later on as the circular hole’s center - e.g. guides or other geometry to snap to.
Edit the group and draw over an edge in the circular hole top and bottom.
This should cause the face to ‘heal’.
Erase the top and bottom circles. which should have now merged into the faces.
Redraw the top circle based on your center-point from earlier.
When drawing a circle you can set its segments at the start - e.g. start it and type say 60 to set the sides, then the radius. Or after the radius is set you can type 60s immediately to change it - but after that it’s likely to have become immutable.
PushPull the circle down through the floor to punch the desired hole…