Thanks for asking about this @sghosh1115
. This is a known issue currently with the Chromium code base (the code that is shared between Chrome and Edge). We are discussing the use case in the public bug you can see here: https://chromium-review.googlesource.com/c/chromium/src/+/3239022
There is some debate about whether this should be a supported scenario or not. I believe it should be, as leveraging --app with --inprivate is a really compelling scenario to me, but you may notice that when you are in an inprivate window we do not let you pin or install the site.
Regardless of all of that discussion, hearing a customer voice that says they like the feature and use it regularly does help.
Engineering Manager, Edge