Originally, Airplay wasn't designed for multiroom applications which changed when Apple introduced Airplay 2. The included shairport open source implementation uses Airplay 2 and should let your HifiBerry work as Airplay speaker from any iOS device.
This is the defacto open source standard for multiroom audio. Logitech media server was designed for multiroom audio from the beginning. If you're ok that the user interface looks a bit old-fashioned and the configuration (especially with plugins) can be a bit challenging, have a look at this.
Snapcast is an open-source multiroom client-server audio player, where all clients are time synchronized with the server to play perfectly synced audio. It's not a standalone player, but an extension that turns your existing audio player into a Sonos-like multiroom solution. You can find the official repository at github.com/badaix/snapcast.
This is the "luxury" multiroom solutions. While Roon, isn't cheap, the sound quality is great and it has very powerful multiroom capabilities. From the Roon client on the mobile phone (or on your PC), you can easily hand an audio session over from one room to another. You can also group multiple endpoints to stream the same audio synchronized to multiple endpoints.