This one could have passed by you without you noticing because it seems to have passed a lot of people by it seems. Twitter, sometime late last year, rolled out Notification Channel support for those running the social networking app on Android Oreo. The problem is, they never announced it or put it in the release notes so it isn’t clear when the new feature came into the app.
Notification Channels, in case you don’t know or remember, allow you to set more granular toggles on the types of notifications you get from an app. It is supported in Oreo but not every app has support for it yet. Usually when a developer adds support, they advertise it. Apparently not Twitter.
Within the settings of the app (go to Settings>Apps & notifications>Twitter>App Notifications) you can no enable notifications for the Direct Messages, Emergency alerts, related to you and your Tweets and Followers and contacts to name a few.
By default, all of the notifications will be enabled but you can mute any of them using these toggles. You can also toggle if you want to have the notification dot enabled so you will visually know if you have a notification.
Finally, if you have multiple accounts, you will have the ability to set these notification channels for each account you have configured.