When does COVID travel isolation/quarantine end? [Germany, State of Berlin]

In general, your local Gesundheitsamt or health authority is responsible for defining the exact terms and conditions of your quarantine when ambiquities such as this exist. You should contact them for authorative information as opposed to relying on strangers on the internet.

In my past experience, my health authority interpreted the rule as the quarantine lasting 10 calendar days from the arrival day (including arrival day which may differ from the departure day.)

The quarantine period starts after entry from abroad

• Event 2. 1755, ten days after my plane arrived at gate in Germany

Note: The quarantine can end earlier if a negative result is returned from a test taken 5 days after arrival.

Einreisen aus dem Ausland: Quarantäne und Meldepflichten
Wer über den Luft-, Land- oder Seeweg nach einem Aufenthalt in einem Risikogebiet in das Land Berlin einreist, muss sich unverzüglich nach der Einreise auf direktem Weg in die eigene Wohnung bzw. Haus oder eine andere geeignete Unterkunft begeben und sich dort für einen Zeitraum von zehn Tagen nach der Einreise ständig aufhalten.

Entry from abroad: quarantine and reporting requirements Anyone who enters the State of Berlin by air, land or sea after a stay in a risk area must go directly to their own apartment or house or other suitable accommodation immediately after entering and stay there for a period of time stay for ten days after entry.

Ende der Quarantänepflicht
Die Quarantäne kann frühestens fünf Tage nach der Einreise beendet werden. Voraussetzung hierfür ist, dass die betroffene Person einen negativen Test auf das Coronavirus vorweist, welcher frühestens am fünften Tag nach der Einreise durchgeführt wurde.

End of the quarantine obligation
The quarantine can be ended at the earliest five days after entry. The prerequisite for this is that the person concerned has a negative test for the coronavirus, which was carried out on the fifth day after entry at the earliest.

Regulations for persons entering Germany in connection with coronavirus SARS-CoV-2/COVID-19:

If you are entering the Federal Republic of Germany by land,sea or air and have spent time in a risk area within the 10 days prior to entry, you are required – bar the exceptions listed below –to proceed directly to your own home, or other suitable accommodation, immediately after arrival and remain there exclusively for a period of 10 days after entry into the country (quarantine).

Each air passenger is required to fill out a form that contains the flight information and date of arrival (Field 4 Ankunftsdatum (date of arrival) of the Aussteigekarte, Anlage 1 (zu § 12 Absatz 1, Gesetz zur Durchführung der Internationalen Gesundheitsvorschriften (2005)) and is the date that will be sent on to (or retrieved from) the responsible health authority. This is a Federal law, based on international health regulations, which is binding for the states to follow in their individual Ordinances (Rechtsverordnungen).

Sources:

• Einreisen: Häusliche Quarantäne, Melde- und Testpflichten - Berlin.de
• Rules for incoming passengers to Germany in connection with Coronavirus SARS-CoV-2 (PDF)