Must be system Abt - from the photos, hard to say, maybe a double Abt. Below, from left to right: rack for the Riggenbach, Strub, Abt (triple version), and Locher systems:

What I found very strange is an electric rack railway where electricity comes from a third rail on one side of the rails, rather than overhead wire.

A battery car is for the non-electric area... It was a kind of mismanagement of resources

Until recently, in Hungary, there were passenger trains pulled by Russian-built locomotives that lacked electric train-heating/board electricity generators - thus generator cars were used.

However, if the train first came from the capital Budapest pulled by an electric locomotive, and had to continue unelectrified, the generator car was only put on the train with the diesel (just this happens on the image above). Then again, I'm speculating, maybe the battery car on your train was charged from the overhead wire during the first 300 km?

_{*Lunatic*, n.
One whose delusions are out of fashion.}