> The Z3 was only general purpose by accident ... ENIAC [..] was the first intentionally general purpose computer

That's a pretty academic take. Neither Eckert, nor Mauchly, nor Zuse knew about Alan Turing’s 1936 paper when they designed their machines. The classification of ENIAC (and the Z3) as a "universal Turing machine" is entirely a retroactive reinterpretation by later computer scientists. John von Neumann knew the paper and was aware of its significance, but he only turned up in the ENIAC project when the design was complete. At this time, Eckert and Mauchly were already well aware of ENIAC's biggest flaw (the massive effort to reprogram the machine, and in fact they came up with the stored-program concept which von Neumann later formalized). ENIAC’s funding and primary justification were for the very specific purpose of calculating artillery firing tables for the military. The machine was built for this purpose, which included the feature which retroactively led to the mentioned classification.