The 12 lead ECG is used for a different diagnostic purpose.
The Apple Watch is positioned as a cardiac event monitor. Those are intended for extended wear and only need to take measurements between a single pair of electrodes to function.
For instance, a Zio Patch is a modern version designed to be compact and unobtrusive.
Here's a comparison between a Zio Patch and the old school tech of a Holter Monitor.
https://www.medgadget.com/2014/01/zio-wireless-patch-may-be-...
One of the tech journalists at Ziff Davis who took part in Apple's heart study ended up being dignosed with Afib by his cardiologist. He wrote about the process he went through.
TLDR: The watch flagged that there was a potential problem, he was given a traditional tape on cardiac event monitor to wear for an extended period to confirm the watch data, and was then diagnosed and treated.
https://www.zdnet.com/article/how-apple-watch-saved-my-life/
For me, this was the money quote: "I've had EKGs a number of times, and there was never any indication anything was wrong."