I don't love that I need to swipe open the sidebar and look over all of my folders to see if any new emails have arrived on the mobile (Android) app. It would be nice if the folders themselves could show up in the main mobile view if they contained any unread mail.

There could be a preview of the subject and sender to let you know if it was worth looking at, and if not, you could swipe the folder away. It would show up again for future unreads. You could have a setting to prevent certain folders from showing up.

Some people might prefer to keep showing certain folders even if they don't contain unread emails as well, so maybe you could implement settings such as "Display folder in main view if there are emails less than x days old" for individual folders, with a preview of the latest emails. Some might even like to just permanently pin their most important folders as well.