If they don't go down the route of implementing a state-level firewall such as China is doing, they're fighting a losing battle. And frankly, if Telegram were inaccessible from Germany, the same people would simply use the next messaging app. There's nothing groundbreaking within Telegram that cannot be replicated.
IMHO, this is the government embarrassing themselves with the fact that they've lost the goodwill of a huge chunk of the population and trying to blame Telegram for it - as if the mindset and communication of those unsatisfied people would simply change/disappear if they were no longer able to access Telegram. Which furthermore shows that today's governments still do not understand the internet.
For what it's worth, the NRW Landesmedienanstalt is busy establishing a DNS-level censorship infrastructure against Pornhub, Youporn, MyDirtyHobby and others [1]. It won't take long until providers will be forced to also add Telegram's infrastructure to that list.
[1]: https://www.spiegel.de/netzwelt/web/landesmedienanstalt-kann...
People on the blocked Telegram channels have denied the Holocaust (including the channel operator himself) which is a crime in Germany, Austria and 16 other European countries [1] or called for the murder, disfigurement or other injuries to politicians [2].
"Anti-mandate discussions" are bad enough, but unlike what went on in Hildmann's channels this stuff isn't criminal so the comparison of yours is a bit wrong.
[1] https://de.wikipedia.org/wiki/Gesetze_gegen_Holocaustleugnun...
[2] https://www.faz.net/aktuell/feuilleton/medien/hunderte-morda...
On the other hand, forcibly removing content for the sake of the content is censorship. It can be censorship that most people approve of - which they usually do when the content is sufficiently vile and irredeemable - but it's still censorship.
And yes, content was censored on. But not only death threats were censored but also holocaust denial, eugenics and inciting hatred against ethnic groups (Jewish groups, specifically).