Daffy,
Though EmilyS726, has already provided most of the details you need for managing these website Push Notifications and tried to explain them, I'll just add some background and provide the official Microsoft page for managing them as additional information.
Manage website notifications in Microsoft Edge - Microsoft Support
When I was trying to answer someone else's questions about these notifications, I fouind this old history article about them that explains where they came from (Google), why they exist and when Microsoft and Apple added them to their own browser, which for Microsoft was likely when they began using the Google supported Chromium Open-source browser as the base for their new Edge browser.
Behind Web Push Notifications: History of Web Push | Braze
So as usual, we have Google to thank for these intrusive advertising popups used by websites, while Apple and Microsoft came along for the ride in order to provide similar support in their own browsers, in Microsoft's case due to the fact they're using the same core browser.
In a deeper sense, these particular popup notifications undoubtedly also use the Toast Notifications interface that Microsoft included in Windows over a decade ago that allows the display of such messages by apps that aren't currently open, which the Website Push Notifications are also able to do. Though it's a technical page, those Toast Notifications are discussed at this Microsoft page and you'll easily see the similarity of the one displayed there to the Website Push Notifications you're receiving.
Toast notifications - Windows apps | Microsoft Learn
You'll note that some others have posted in your thread about 'rouge' applications or browser extensions displaying popups, which though possible are far less common nowadays due to the fact that Website Push Notifications are displayed by Windows itself once you initially press the "allow" button on an initial; popup that's displayed, meaning they aren't malware as such won't ever be detected by any antivirus or similar security app as malicious. That's why the malicious advertisers love them, since they're just an HTML popup and won't be automatically blocked for you if you press the Allow button by mistake, as many people do.
Though that last image in your first post looks like it might not be a notification popup. I suspect that it was simply launched separately by the other 'Scan in Progress' Website Push Notification' popup that clearly is due to the website and OK button displayed first.
Yes, the combinations here can be complex, but that's the point, since the last thing the malicious advertisers want is for any of this to be easy or seem obvious to allow you to fix the annoying popups without contacting them, so they can either sell you something or steal your personal information or identity, which is often their true goal.
Rob