I once hit a button on a news website that said something about do I want to get notifications from them, and I now get little, well, notifications from them, on the bottom right of my screen every now and then.
I want to go find similar links from other news sources. What do I google? I tried “news notifications” and there’s a lot of different means of notification that are discussed at various links, but I’m looking for this specific notification service, and I need to know its name.
What browser are you using? If you’re using the “standard” Microsoft browser, with Windows 10 that’d be Edge.
What you describe sounds like Web Push Notifications, which is supported on Edge, Firefox, and Chrome. This has to be implemented at the website; you can’t force a website to give you push notifications if they haven’t installed and configured their framework to support it. So if a news website isn’t offering you a notification channel, you can’t get notifications from them. (Assuming I’m guessing right.)