Nope, for latency and battery reasons this would be done by a specific chip, e.g. https://www.icstation.com/audio-module-bluetooth-compatible-... / https://www.tinyosshop.com/ts8670
The same's true on the smartphone transmitter side.
That 2nd link you shared, has 3 links under "Documentation" to firmware downloads.
Or the speakers themselves, eventually
This sounds like something could be done with a firmware update.