Congrats, and welcome to the club.
In 1969, the 340 was available in packages other than the Formula S. It could also be part of the 'Cuda package, or just ordered as an optional engine.
See the footnotes under the engine specs.
https://www.hamtramck-historical.com/images/dealerships/DealershipDataBook/1969/69_Barracuda0007.jpg
If the V8 fender emblems look original, I'd be inclined to think you have a Barracuda with a 340, not a Formula S or 'cuda 340, because they each had their own emblems.
Thanks to
@Alaskan_TA there's a lot to read on Hamtramck Historical.
The 1970 Hamtramck Registry - 1969 Plymouth Dealership Data Book - Barracuda
