I agree with you on everything, except 94% is out of date. 35% of ICU patients are now vaccinated, 46% in the 60+ age group. And the percentage keeps rising, especially in the most vulnerable group > 60.
Check out their weekly reports, the relevant tables are usually around page 21 or 22. In the most recent one, it's on page 24.
https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus...