Pics...
It took nearly a day to do but bearing in mind my Mum is an OAP who is not a builder/carpenter by trade and just has regular DIY level compentence and I am a DIY dunce
It was actually quite easy, the first thing was two batons on each wall, the batons had a 'channel' dug out where the two side panels slotted into and were screwed in. A door was then attached to each side panel. We added the top bit as at the time one of my cats was very athletic and I think he would have easily jumped over. The top bit was just a baton across with a thin channel dug out and and then a bit of painted plywood slotted in. If you wanted to make it look a bit more preofessional you can use plasterboard sheets, third pic is of doors she put in her own house and built plasterboard bit above it herself

She did hers after she did mine so I complained about my sub-standard workmanship

If I wanted to remove the whole thing there would literally be four screw holes on either side to fill on the walls. I think it would have taken 1/2 a day but it took a bit of extra time as my Mum had to use a circular saw to cut strips off the doors as they didn't quite fit

There is enough room to get upstairs when the doors are closed, the angle of the pic makes it look a bit tight but even with both doors closed you can get up/down the stairs. Due to space issues the doors open different ways, second pic is of both doors open ie when I'm home.