I just got my S6 the other day, and immediately installed Nova Prime and Tesla Unread ... and like above, badges are working pretty good except for the Samsung email app, which is disappointing. I have not tried the new beta version yet - but per Kalvin Kerns that doesn't yet solve the issue.
I have used Missed It! before, but if I recall that uses the notification bar to put a badge up, much like the newer function in Tesla Unread ... which means that it's not an "unread count" ... it's just a badge that shows you on the app icon that there are pending notifications for you. As soon as you dismiss the notification, the badge goes away.
True unread-count badges for Samsung email app work perfectly fine on my S4 running Kit Kat ... just no joy on Lollipop yet.
Another thing to mention ... I tried the new Motorola Nexus 6 for a few days, and the gmail app actually allowed you to setup an exchange server account along with your gmail accounts. That was amazingly cool since I could put all emails in the gmail app ... not to mention that the gmail app on THAT phone had an "unread" folder thingy you could sort by. I was REALLY hoping my S6 gmail app would be the same, then I'd not have to use the samsung email app for work. But, as luck would have it, no joy there.
Is there a way to get the gmail app for the S6 that allows you to setup an exchange server account? If so, that would solve quite a few problems for me all at once.