Seiko says SR726SW is spec which apparently equates to 397. It had an SR721SW inside it (which is apparently 621). I haven't looked up the specs of those batteries, but they appear to have identical diameters - the 726 is just a smidge thicker.
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I have a DW-1000 with a 280 module, which takes a 2020 lithium battery. It had a 2016 inside.
Both 397 and 2020 are odd batteries...I had to go on Amazon to find them, and there were not many sellers/options for either. I have no doubt that you are right, the watchmakers took what they had on hand based on diameter size and tossed it in.
I am usually the kind of person to be like "let the pros do their job" but this kind of stuff has me taken aback. I think it's funny that I figured out two watches in as many days.