Consider getting Chromecast Audios and cheap speakers through your house and creating logical groupings (e.g. I have an "everywhere" group, and common room paths + destinations for various things, like Living Room through Hallway to Bathroom), and using the Cast feature of PocketCasts. Much cheaper than Sonos, etc. and you probably have a bunch of speakers anyway. Also Google Homes double as a good enough speaker in annoying rooms that don't have many outlets, if you're ok with having a microphone in those rooms, and they obviously synergize well with the Chromecast Audios.
(I am very happy with my wireless headphones.)
Battery life is probably an issue too, but with low power wifi SoCs like the espressif stuff, you can probably get away with similar to Bluetooth using the tech that's around now and doing as much possible in hardware and with interrupts as possible.
I'm really curious if this is a special function of the AirPods or Apple's W1 bluetooth chip in general. One of my other pairs is an older pair of PowerBeats sports headphones. I would definitely consider replacing them with a new set of BeatsX headphones if that's the case.
Maybe this?