It was very likely one of batteries where each 'cell' looked like a block of compressed charcoal, about an inch or two square, with a strip of plastic around the edge. When I was a kid back in the 1960s, we used to pull these apart and throw the cells around like stones.
The most common size radio battery then was a 45 v battery, about 7" x 5" x 2" (IIRC) with a small socket in the top of it. https://www.flickr.com/photos/unclegal/31122957375
I'm also very surprised that it's not corroded.
[1] https://en.wikipedia.org/wiki/Zinc%E2%80%93carbon_battery
Beautiful bit of history, thank you very much for taking the time to do this one.
If it was for reliability, I'd expect the emitter to also be doubled, but it has a single wire.
GE made the 3N36/37, but here's a datasheet for a similar part: http://bitsavers.org/components/ti/discrete/transistors/3N34...
The beeper is one of those crystal (piezo) earphones with part of the bit that you would stick in your ear cut off.