I had the Pebble app running for a long while without any issue whatsoever, just didn't opened it as I didn't had a need to install new watchface or app. Today, I opened the app to check the app version as someone said to me he was experiencing huge phone battery drain caused by Pebble app, after opening the app now my phone has the same issue.
Fortunately, installing a previous version of the Pebble app did it for me, here's a link to version 4.2.1-xxx if anyone wants it :
The version I had before was 4.4.0-xxx, which was the latest version available on Play Store for my device. As someone else said, reinstalling the app or logging out and back in didn't fixed anything on 4.4.0.
Phone is back to normal now, and as of now I can't see anything missing or not working. Let's hope we'll be able to use our Pebble for a long time.