After rolling an integrated browser out to some users recently, Twitter now appears to be testing a floating action button (FAB) in the app. This takes the place of the new post bar that hovers at the bottom of the screen in the current official version. It looks much nicer.

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Left: New, Right: Old

You can see how the FAB compares to the current bar in the screens above. It seems to be a better use of space. Twitter still doesn't use a navigation drawer, but at least the status bar is colored on Android 5.0.

If you want the FAB right now, it looks like you're out of luck. It's server side just like the browser. There are some beta and alpha builds of Twitter on APK Mirror. You're welcome to try installing them to see if that triggers something, but I installed the newest alpha and no dice.