For what its worth, I was pleasantly surprised by the things you can do digitally in Kiel.
Schleswig-Holstein, Niedersachsen, Hamburg and Bremen have "Dataport", a publicly owned company which does a lot of the tech for public institutions in the area. While they are not operating at the efficiency of a normal company, they seem to be fairly useful. I'm not sure if something similar exists for other regions in Germany.
Now this has changed a lot in the last decade or two, but it has been accompanied by avg. yearly net migration of 80k people which is putting a major strain on all public services.
Berlin isn't centralized, but the districts (Bezirke) have quite some freedom to structure their work (similar to "kommunale Selbstverwaltung" in other states) and how they run the administration offices (Bürgerämter etc.) which then leads to city administration passing a law for something and each district implementing it differently and city administration having no authority to override district decisions, while taking the blame.
Fixing this requires a change to the constitution, but that requires a 2/3 majority in the city assembly (Abgeordnetenhaus) or a referendum. Getting the majority is hard as there are varying differences (from parties being happy about number of posts to full, like district mayors etc.) and "dislike" between districts (East/West, center/outer, ..)