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I agree that this is a long and rambling document. Thanks for posting this document so people can see it and make up their own mind. I have seen the German original and this translation follows that very closely in the key part of relevance here. I too got the impression when I first read it that people who are double vaccinated are allowed into Germany. And that is true, but it goes on later to say that people who have been in a high risk area within the last ten days must also quarantine for ten days, 14 in the case of new variant areas. The key sentence, in my view is:
'In addition, when entering the Federal Republic of Germany following a stay in a high-risk area or area of variants of concern outside of Germany, a special obligation to register, quarantine and furnish proof has to be observed.'
At the end of the day, this is not too surprising; travelers entering the UK from our list of red list countries also have to quarantine for 10 days in a hotel even if they are fully vaccinated.
My interpretation is different as I have read the whole document
It does say 10 days as you correctly state but further down waivers this requirement if one uploads a vaccine passport
Ending quarantine: Quarantine at home may be ended early if proof of recovery, proof
of vaccination or a negative test result is submitted via upload portal of the digital
registration on entry at
https://www.einreiseanmeldung.de. The individual link on the
registration confirmation (PDF document) should be used to upload the proof of recovery,
proof of vaccination or a negative test result. Quarantine can be ended in each case from
the time the negative test result is submitted. If you spent time in a high-risk area prior to
entry, the relevant test may not be conducted earlier than five days after entry (test to
release possible from day five following entry). Vaccinated and recovered persons can end
the quarantine from the time when the proof of vaccination or recovery is transmitted via
the entry portal. If the transmission takes place before entry (strongly recommended), no
quarantine is needed.
• Following a stay in an area of variants of concern, the duration of the 14-day quarantine
may not be shortened.