Any progress in establish whether the song is, in fact, language?

I remember walking early morning last summer, listening to the birds and thinking how absurd it is to believe this isn't a type of language.

I guess it would depend on what is considered the minimum constraints to be considered a language.

ML techniques are leading to some interesting work in determining this. Here's one such example https://journals.plos.org/ploscompbiol/article?id=10.1371/jo... Female zebra finches do not sing, only males do. I'd imagine that if bird song is high on communication, it would be seen in both sexes (and there are song birds where females sing, but not studied as much as far as I know.) tldr: still unclear, but new techniques give us hope we can answer

I wouldn't be so quick to write off birdsong as speech based on this one species—given the dramatic variability in form, behavior, and habitat across the animal kingdom, a particular family of birds where the males don't "talk" wouldn't surprise me at all.

Absolutely. Agree there's a lot of variability. Only pointing out that in species where only males or only females croon, it may be unlikely there is broadspectrum communication happening.