Sadly, I think the new name for this kind of thing has been "literate programming" for the past 20 years at least, while the literate programming that Knuth described has been renamed something like "the literate programming that Knuth described".
I think Docco was when that approach acquired some kind of popularity? So 2010 or so[1].
Of course Haskell has had its “literate format” since forever (ETA: the Haskell 1.2 report[2], dated March 1992, has a description in an appendix), and it became mildly popular for Haskell blogging when blogs caught on, but its name was always accompanied by a side note that in Haskell you don’t really need to reorder things (kind of true).
I recall, on first encountering Literate Haskell at some point after 2010, mentally comparing it to something I thought I recalled from earlier in the perl ecosystem (on top of being vaguely aware of Knuth's stuff, although I hadn't actually read up on it at that point - at this point I have a copy on my desk).
POD? I’ve only encountered people using it to embed manpages into their single-file scripts, even if it turns out that the documentation[1] doesn’t consider this the canonical use case and demonstrates something much more like LH. But then I’ve never done much Perl.
