ISO 8601 is proprietary and people can’t even read it without each paying a $170 access fee. Instead, prefer IETF RFC 3339 (mentioned in your link) which is a more practical open standard.
In prose, use month names (i.e. 1st Jan 1979, or Jan 1st 1970). Where numbers must be used for some reason use four-digit-year first if you can. If you can't use the dictated standard or, if there isn't one (raising the obvious question of why that would be), go with the form that will be familiar to most of your readers.
In other words, as with all things, prefer unambiguous forms but consider and respect your audience.
How do British people pronounce the date that they write as 15 September, 2021? Americans write the date the same way we pronounce it (September 15), but this leads to the unfortunate mm/dd/yy style of abreviation.
As I was first looking at my post, I did have that mental flip/reverse-aphasia take place where you don't know how that spelling is even a word. I wonder if some German was adding to the ambiguity.
