That’s a good observation- my thought is that is a handle, expandable since the inner ears allow it to slip in and out
I have quite a few reference books, but not all of them cover the IW period. I was able to find something that looks very similar, but I can't say for certainty it's a match. The item I found was a cover for a case that held field binoculars. I wouldn't say it's solved, but that might help with your research.
Here they are. While I think the cases are made from thick leather, it appears the bottom is some type of metal and, in my opinion (without having ever seen one up close), some type of stiff material would be necessary for the case to hold its shape under field usage. I've looked at all the photos in my reference books for cartridge boxes as someone suggested it might be a lid for one of those....and it very well could be, but all the ones in my books have folded leather covers held in place by a catch (Google Dyer cartridge box for an example). As I said earlier, I'm not certain it was used on a binocular case, but those dimensions you listed certainly seem close to the width and depth of binoculars from that period.
That is Very interesting and has merit-
