> If an old coin is deemed to not be historically significant, it probably belongs to the landowner.

According to § 984 BGB, a historically insignificant find belongs to the finder and landowner in equal shares.[1] If the find is so important that it is considered a "cultural monument" (Kulturdenkmal), the law of the individual German state determines who owns it and whether or how much of a compensation is payed to the finder.[2]

[1] https://www.gesetze-im-internet.de/bgb/__984.html (in German)

[2] For details see https://de.wikipedia.org/wiki/Schatzregal#Deutschland (in German)