Nothing wrong with not revealing the views upon entering. It makes a nice surprise for wanted guests and keeps thing private from others. Make the entry inviting, which it is. Possibly move the credenza a little to the right and add a little art behind the credenza and a nice rug, maybe a plant.

"Should we consider floating stairs?"

Certainly, if you've got the budget. 30K +-.

"Will that be too open?"

I doubt it.

Yes, move credenza to the right and lamp to the left.

Is there anything under the stairs? Basement access or storage closet?

An open staircase could look good, but probably not worth the cost of the project.

thank you - feeling better about keeping the structure as is and just modernizing the staircase.

Floating stair makes the space bigger.