Well, that's mostly the case.
Hate speech is not about stating that you "hate" a group of people. That's protected by your freedom of expression in Germany. You may also insult or offend people based on race, colour, ethnicity, sexual orientation or whatever. And while there are lawsuits here and there filed in those cases, they're usually dismissed. However what's not protected and classified as hate speech is if your speech includes threads of violence or similar things, that are covered by coercion laws. In German the expression for this is "Volksverhetzung" which loosely translates to 'incitement of the masses'. Another expression is 'Hassprediger' which translates to hatemonger and describes people that incite hatred or violence towards other people or groups. Holocaust denial is the really special case in Germany, that should disappear soon. The more time goes an, the fewer people's experiences get denied and ridiculed by this. The original intention to get rid of the remaining Nazis, was also fulfilled. There's no practical reason to keep this up any more besides of censorship of people who want to publicly declare that they're ignorant of a lot of evidence.
The weird thing is that there are already laws that cover these things. Individuals can be persecuted, although they rarely get convicted. So why trying to make platforms liable? The answer is simple: Next year is election year and politicking, as in doing things for the sake of appearing to care for the people, is a very popular move in politics.