What was the first aircraft designed with a plug-system fuselage, and why?
This should be a Zeppelin. You said "aircraft", not "airplane", so lighter-than-air systems qualify also.

Already the model submitted with the patent application in 1895 (yes, back then the inventor had to demonstrate that the invention is actually implementable!) showed several cylindrical sections, akin to a train of cylindrical balloons. The final patent (Reichspatent No. 98580) was for a "Lenkbarer Luftzug" (dirigible aerial train). Adding more sections would increase length and payload.

Later, when the maximum diameter of Zeppelin airships was limited by the size of available hangars, their mid section was of constant size and allowed to add plugs to increase payload and range. This was, among others, the case with LZ 104 which turned out 30 m longer than initially planned.

The last big airliner not designed for stretching was the Lockheed Constellation. It had a continuously varying cross section from tip to tail.