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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.
If you read the Foreign Office travel advice for Germany, it seem pretty clear that:-
- If you are fully vaccinated, you can enter Germany without a test beforehand, and without the new for quarantine.
- If you are not fully vaccinated, you can only enter Germany if you satisfy their list of exemptions. It is those people to whom the 10 day quarantine applies.
For those individuals eligible to enter Germany who are not fully vaccinated, travel from the UK is generally subject to 10-day quarantine with test and release available after 5 days. Both individuals who can prove recovery from the virus and the fully vaccinated are exempt from quarantine requirements.