FYI, for anyone interested: Tapatalk support got back to me with this message:
Thank you for contacting Tapatalk. The issue is currently still being worked on by our technical team. Please accept our apologies for the inconvenience this is causing. Our team should have it fixed shortly. Chris Tapatalk Support
So, seems to be a problem on their side..?
Also, to clarify: The problem isn‘t the notifications, but rather that subscribed topics won‘t be updated anymore (since June 2nd for me).