They have corrected this yesterday by releasing Version 6.0 which is also apparently a PWA (Progressive Web App) which, if you have alerts enabled might have been obvious as it informs you that a login via Microsoft Edge has just been completed.
While this was the biggest request from users in the Feedback hub, it did have other issues. Live Tiles are a big part of Windows 10 apps but Twitter previously only actually showed tweets and images from tweets (both of which made things slightly more interactive and pretty) if you were logged out. If you were logged in it only showed you notifications even if you have read and dismissed them on other devices. You would have to go into the app, read the notification in there, while having the start menu open and it would then go back its default blue live tile.
Overall an improvement and nice to know it hasn't been abandoned, hopefully there are future enhancements forthcoming, there are very few interesting Windows 10 apps to populate the Start Menu so the most popular really need to put the effort in.
View Microsoft Store