A couple of weeks ago, Twitter updated its alpha release version to add several of Android Nougat's features. Now these options have made it onto the stable release version of the app, so you no longer need to live on the bleeding edge to benefit from them.
Version 6.22 of Twitter is the one that brings it all. There are Android 7.1's launcher shortcuts, which you can access if you're using the Pixel, Nova, or Action Launcher, as well as a rounded icon that will likely only be visible if you have a Pixel or if you're running a launcher that supports them.
Multi-window support is also officially implemented, meaning you can browse Twitter and use other apps at the same time. If the Play Store version hasn't updated to 6.22 for you, you can grab the file from APK Mirror and install it manually on your phone.