Yes you can still see badge notifications in the App Library, they are just turned off by default for some reason. Open Settings -> Home Screen and toggle on Show in App Library.
If you use the News app and follow multiple channels, and you have notifications turned on for each of them, you are probably inundated with alerts of breaking news stories. While you likely dismiss most of them, there are probably a few that catch your eye as something worthwhile, but you either don't have time to read them at the moment or aren't in an appropriate setting to do so. If such is the case, you can always save stories to peruse later - a great way to curate a reading list for when you have some down time.
This afternoon many iPhone owners across the US are wondering why their devices received two emergency notification tests. So-called Presidential Alerts are sent by the Federal Emergency Management Agency (FEMA) to all wireless subscribers nationwide. Unlike normal Emergency Alerts and AMBER Alerts, these Presidential Alerts cannot be turned off.
All wireless providers deliver government-issued Wireless Emergency Alerts (WEA) to iPhone owners on their networks. The capability to receive these alerts was added with a Carrier Settings Update in 2013. There are three types of alerts, two of which iPhone owners can turn off.
Notification badges are great at doing their job - letting you know that there is something you need to look at in the notifying app. The problem is they can easily become overwhelming if you have tons of apps constantly demanding attention for every minor event. While you likely want to know when new emails are sitting in your work inbox, you may not want to know every time your troops are ready to battle, or every time somebody has posted in a Telegram room with 10K subscribers.