I should have said "commercial hardware implementation" instead of just "hardware implementation" because I was excluding Z1 (as something that didn't really work, so not an implementation) and Z2 (as something which was only a prototype for the Z3 (and a demonstration machine for the German military), not a properly engineered machine. I don't regard the Z1 as an implementation (because it didn't often work, or so I was told).

Although construction of the Z1 started in 1936, it didn't finish until 1938 and even when finished the machining of its parts wasn't clean/accurate enough so the machine frequently went wrong (or at least so I was taught long ago). There was no working Z1 until Siemens worked with Zuse to build one that actually worked (rather than reconstructing one that worked sometimes) in the late 1980s (a valuable history project, I think).

The Z2 (finished in 1941) was another one-off prototype, with no future - it sprawled over too a large space and was very much a string and sealing-wax piece of engineering - in effect it was the testbed in which some of the Z3s design was verified.

The first working machine, which actually went into production, was the Z3 (also 1941), and that was the machine I meant.

Although it wasn't what we today call an electronic stored program computer, it had a significant electrical component (mechanical relays) and did store program in its electromechanical store.

Zuse had patented pretty well all of what is known as Von Neumann architecture a few years before Williams and Kilburn started developing a reliable non-mechanical store for a stored-program computer which in turn was a year or two before Von Neumann wrote his report. In fact floating point was probably the one area (apart, of course, from politics) where Von Neumann disagreed with Zuse - he was famously anti-floating-point.