Incoming infodump. I agree with another commenter that Auracast ist exactly what you want, problem: barely available.
Bluetooth is split into 2:
Bluetooth Classic
Bluetooth Low Energy
Auracast is a very new standard using BLE Audio. I've seen some aliexpress sellers selling Auracast hardware for silent discos. But from well known brands I haven't seen a thing
Most BT headphones you buy use Classic, and cannot achieve multiple connections. So no built in solution.
Obviously there are proprietary Technologies that had custom transmitters/recievers for this exact usecase.
TLDR: If your Phone can do BLE Audio you could gamble on some Auracast hardware from aliexpress. Else, look for premade solutions not using Bluetooth
Oh no, project sekai has broken containment and jumpscared me on my fediverse timeline
( I think this meme might be a useful template for this community )