The iOS 13 page only states this is compatible with AirPods, and it’s not clear if it’s supposed to work with other devices.
Pair two sets of AirPods to one iPhone and enjoy the same song or movie along with a friend.
* Works with iPhone 8 or later and iPod touch (7th generation) with the latest version of iOS.
Regardless, the choice to connect to multiple headphones is handled through the native AirPlay menu. Are you able to select both of your devices there?
Audio sharing is compatible with: AirPods, Powerbeats Pro, Beats Solo Wireless, Beats, Beats Studio Wireless, and Powerbeats Wireless.
Audio sharing can only be used on iPhone 8 and later, iPad Pro 12.9″ second generation and later, iPad Pro 11″, iPad Pro 10.5″, fifth-generation iPad, third-generation iPad Air, fifth-generation iPad mini, and seventh generation iPod touch.