This is true unless you look at something like a Seiko Spring Drive, which has a completely smooth second hand sweep, although it’s not entirely mechanical (and maybe only watch nerds care about this)

https://www.hodinkee.com/articles/does-spring-drive-have-an-...

Pedantically, only above second granularities. They're continuous between second hand sweep movements at subsecond ones, no? I mean, there's no point on the watch that the second hand doesn't "hit" at some point, however small.

Or am I wrong that "intermittent, jerky, continuity is still continuity"?

Well it depends on the interval. Taken to the limit, this would be a very nerdy way to rediscover calculus.