This may be an Edge error, or it could be an NVDA error.
I just tried this and while SHIFT+F10 definitely brings up the context menu when NVDA is running, focus does not shift to it, but remains on the page in Edge itself. This is not the case when NVDA is off. If I do SHIFT+F10 without NVDA running, and hit either up or down arrow, I am traversing the context menu.
It's not clear to me if this is an NVDA bug or an Edge bug. But since you say you get the same misbehavior with Narrator, I suspect that something is not being exposed to the screen reader by Edge that should be that allows the screen reader to have focus set in the Context Menu when it appears. I don't have JAWS on this machine, or I'd try a quick test with it. I suspect the same issue would present itself, which would really point the finger at Edge (or something in Windows that Edge depends upon for context menu presentation).
Brian - Windows 10, 64-Bit, Version 21H1, Build 19043
I do not understand why some seek to separate a person from their actions. The self is composed of an individual’s thoughts, actions, and expression, which are contained in and actuated by the body. What you do and say is the clearest indicator of who you are.
~ Brian Vogel