Bluetooth audio latency, codecs, when does it matter

These are some random-ish observations regarding Bluetooth audio latency vs "codecs". This started life as a long comment trying to untangle a messy thread in Wirecutter's review of bluetooth speakers, but since it covers a lot of things that I periodically forget about, I'll have it now as a refresher for myself next time I'm checking BT headphones.

A couple of pre-clarifications:
  • Different people measure different things, sometimes without even realizing, so it's important to make sure that one understands what a number means. Algorithmic delay? Hardware (+firmware) implementation? Hardware + software? Which software: OS + encoding + decoding, or just the OS piping things around? Is there some app involved? Each layer not only adds delay (lag, latency), but also variation (jitter).