Does one take on duties from the previous owner or previous resident?

I will report on how it develops.

Thanks again for your assessments!

to summarize:

- the hedge is not on your property
- there is no building encumbrance or other notes in the land register about this hedge
- the former owner somehow messed something up during GDR times
- the hedge was never mentioned in the property purchase contract

the chances are certainly very good that the hedge is not your problem. if anything, the municipality must contact the old contractual partner. due to the lack of connection to the property, anyone could have planted or maintained this hedge there.
in case of emergency, however, you should consult a lawyer in advance. the municipality will probably tear it down and try to claim the costs from you.

The argumentation of Escroda seems convincing to me. The initially mentioned basic attitude of wanting to avoid conflict is also important, in my opinion. The city occasionally needs areas for compensatory planting due to tree felling elsewhere. A row of chestnut trees on the municipal green strip, for example, will cause you more long-term trouble, leaves, darkness, ... than the hedge.

Property is often not about what something stands on, but who it belongs to.
Commonly seen and understood in boundary construction.
If I plant a tree on your land, it is not yours, but mine

that is nonsense, look in the Building Code, it states what property is and what is only a notional component.

Sorry for the late response, we were quite stressed. But there is news:

Just a few days after the last post here, the landscaping company came and trimmed the hedge again! I don’t know why they only came now (in previous years they always came twice, once in late spring and once in late summer/autumn about), but apparently the lady from the civil engineering office didn’t pass on anything or whatever - however this came about: We hope that the city continues to trim the hedge and that it was not only because, for example, the city always contracts in advance for the following year and that is why they only came again this year.