It is a kind of fallout from a long overdue reform of that law area. In theory you even have to stop 'sending' your website between 6:00 and 22:00 if it contains adult content, same law. The reform failed due to the totally insane requirement of rating every single website for child protection. As it is a law with state and federal parts, you have lots of duplications and weird rules.

So the 'register all XMPP clients' is a side effect of german regulations that still consider Internet to be mostly just a slight variant on Phone&TV&Radio.

In the past (1980s/1990s) you had (in theory) to register any BBS service as a telecom provider, but they didn't even have a proper form to do the registration.