Most regions have their own prevailing construction methods and materials that are common and customary to that region. It may be driven by the available raw materials, local labor and their experience with a certain type of construction, and the cost of labor to build. Other factors that drive the different type of construction can be pressures from the environment and climate conditions. One can create recesses in masonry or stone walls but there may be structural weaknesses that become a factor or just more complicated construction that becomes involved. Building recesses in heavy masonry walls verses light stick framed walls can be equally possible. Reducing the thickness of a wall can also affect the insulation capabilities of that wall as well as the structure.

is it a curved staircase? What is the highest point of the staircase? maybe you can do something like this image:

Upholstery and egg crate type foams will not be rigid, and may not be flame retardant. EPS and XPS construction insulation foam are lighter weight, more rigid, and could be covered with batting and fabric. They come in 4'x8' sheets, but can be cut with a utility knife into smaller sizes. They are available from a big box home improvement store like HD or Lowes. Not sure if they are flame retardant. Depending on how large a piece you are mounting, I would think they may be light enough in weight that they could be mounted to the wall with 3M removeable hangers of some sort.

My first suggestion would be to change the layout of the room at bit. this is my suggestion:i also think that you should paint the room in a uniform light colour (preferable white) and also paint the wardrobe in the same colour so it doesn't overpower the entrance and blend in with the room. my second most important suggestion is to increase storage. here are some ideas for that: simple plank shelves with filing boxes and folders with labels can be a cheap and efficient way of storage of study material. here are some links for such folders and boxes: https://www.amazon.in/Elan-Bookshelf-Executive-Certificates-Certificate/dp/B00HWRHKOS/ref=pd_sbs_79_11?_encoding=UTF8&psc=1&refRID=BQE8PBQNYQYXHHDEBAVQ https://www.amazon.in/Corpac-Multipurpose-Durable-Plastic-Storage/dp/B01GBBHT1E/ref=pd_sbs_229_40?_encoding=UTF8&psc=1&refRID=1CC92M79MCJDPWBD53H9 https://www.amazon.in/Aristo-Basket-Medium-Without-Multi/dp/B06WGR811H/ref=pd_sim_229_4?_encoding=UTF8&psc=1&refRID=JD75V1WW64930CV4NG69 Also the sunlight is the biggest asset of the room and yet the aluminium window is an eyesore. so i would suggest some nuetral shade curtains. and you can play with the colors of the room with the bedsheets. And agree with studio chippan's suggestion of a painting or a family portrait or frame certificates of the kids achievements. Best of Luck, Purva Saksena (Architect)