So I got curious and went down the Wikipedia rabbit hole. Here's the first paragraph from the apple butter article:

The roots of apple butter lie in Limburg (Belgium and the Netherlands) and Rhineland (Germany), conceived during the Middle Ages, when the first monasteries (with large orchards) appeared. The production of the butter was a perfect way to conserve part of the fruit production of the monasteries[1] in that region, at a time when almost every village had its own apple-butter producers. The production of apple butter was also a popular way of using apples in colonial America, well into the 19th century.

So yeah, apple butter has roots in Germany, at least for central Europe. However, other fruit butters have other origins, such as Lekvar and Powidi, as you mentioned. At the same time Latwerge and Apfelkraut were developing in Germany, monasteries in the British Isles were also developing apple butter as a preservation technique. It seems the tradition/technique developed in parallel as a communal way of preserving fruit.

Since grandma's recipe included a sweetener it likely has its roots in the British Isles, where honey would be added to the preserves as a sweetener. Her apple tree produced a fairly sour soft apple, which also would inform that decision. The pies were amazing