Good evening, Brian.  Singing bird cages have been made since the
late 1700s (Jaquet Droz) and are still made today (Reuge, MMM and
a few really poor quality Chinese mechanisms).  All bird cages crafted
post-WW2 have synthetic parts except for Bontems and a mystery Japanese
maker that copied the Bontems design.  Bontems stopped production in
the late 1950s.  Some German bird cages made pre-WW2 also had synthetic
parts.

The bird cage you referenced was most likely made by Bontems of Paris,
France.  The embedded video did not work for me so I could not hear it
play.  However, looking at the number of cams on the movement, this may
play more than one bird song (shifting cam).  I say this because there
are more cams present than needed for a single bird to animate and sing
one song. The photos are not entirely clear but it looks like this may
have four, possibly five cams.

Kind regards,

Troy Duncan