i don’t think either is correct. the leap second is an extra second, that’s it. the notation for the extra leap second is lacking so we are “forced” to call it 23:59:60 but that doesn’t mean that minute has 61 seconds. it just means after that minute but before the next one, there’s an inserted second.

it’s far more sane to define it that way than to say the duration of a minute (and hence hour, and day, and week) is variable.

I see what you mean but how do we address that leap second specifically? How do we describe an event that happened during the leap second?

Well, it could also be the case that some minutes have 59 seconds, although afaik it hasn't happened yet.

Given the trend of leap seconds, I don't think it will happen (unless we do really stupid things to the earth). See https://what-if.xkcd.com/26/