set your screensaver to 1 minute while testing. that cuts down on the time to diagnose which process it is.
for Edge, check out Settings --> System and see what the state of "Continue running background apps when Microsoft Edge is closed" is. if it is on, turn it off and see if that solves your issue. i thought i had read this somewhere else.
Yes, I tested both with SS and screen time out set to 1 min.
On the other hand, when I setup my computer I looked for that setting in Edge but I couldn't find it. There is General, Privacy & sec, Passwords & autofill and Advanced. No System section, not even inside these sections. I remember setting this up on other Win10 Edges on other PCs (I work on IT).
I also looked for it in Windows Settings (the Control Panel replacement thingy)/System... The most similar was Settings/Privacy/Background apps. But nothing like the Google Chrome option "Continue running background apps when closed".
Oh, and Edge was not the culprit so far. It is running again by itself but the SS worked.
the version i have is: Version 85.0.564.68 (Official build) (64-bit)
this version is based on Chromium. maybe your version of Edge is not the latest that has Settings --> System.