I made a small sketch of how I made the interior walls.
the brown is the box wall and bottom. Grey is cardboard to fix the cloth because if you glue it directly the glue would come through the cloth. I used 2-3 layers ad cardboard. If you want to make it more thicker can make more, of course. Pay attention to measure and cut out as accurate as possible to avoid gaps or too large and won't fit inside. Of course test fit before glueing.
Red is the cloth. Green is where I applied glue. Pattex works fine for something like this. First glue #1. The cloth on the cardboard, let it dry, then wrap the cloth around and glue it against the wall (#2)
After dried can press down the cloth towards bottom to make it tight fit and glue it on the bottom. Repeat for all walls. The bottom I used a old mousepad (yellow) to have something more soft. Cut it to fit in and also wrapped it with the cloth.