So I’ve had a similar problem where not only stairs, but any any overcomplicated piece of BSP after saving and closing. Not only can I only select faces when clicking the BSP in the viewport, but trying to copy or even center focus with the ‘f’ key are impossible.
That said, I did come up with a very peculiar solution: Select the BSP in the scene outliner. Alt move the object to create a duplicate. Now you can select the duplicate AND the original as normal. Then you can delete the copy and continue with your work. I don’t know if this solution is permanent, but it might just be a bug that needs fixing. Let me know if that works.