I went to this site from UK government
https://www.gov.uk/foreign-travel-advice/germany/coronavirus#:~:text=Testing%20positive%20for%20COVID%2D19,those%20who%20are%20fully%20vaccinated.
This is what is said:
Testing positive for COVID-19 in Germany
Anyone testing positive with a Point of Care (PoC) antigen test is required to take a follow-up PCR test immediately and to self-isolate. Close contacts are also required to self-isolate, although exceptions may apply for those who are fully vaccinated.
In the event of a positive PoC test, the test provider is required to notify the local health office (Gesundheitsamt), which is responsible for monitoring self-isolation and will provide further guidance in individual cases. You can find your local health office by postcode here.
Individuals testing positive must self-isolate in their home or where they are staying locally, or in another appropriate location enabling self-isolation. They may only leave their home and interrupt self-isolation to carry out the PCR test. Germany does not operate a system of managed quarantine in government facilities.
Mandatory self-isolation ceases after 5 days. The German authorities recommend staying in self-isolation until you test negative with a rapid-antigen test.