Hi,
Incognito is meant to automatically clear your browsing activity after you finish. If sessions were allowed to continue, some data would end up being saved, which defeats the purpose. If you’d like to keep a private session going even after closing Edge, it’s essentially the same as creating a separate Edge profile. That way, you can browse freely and just clear all the data when you’re finished.
If you have a different idea of how you want your private session to work, I highly recommend submitting it via Feedback Hub app (pressing Windows + F) in addition to what 彭迪斯 mentioned. The more upvotes you get, the more chances the Edge team will consider it.