Is there a way that 3 people, all with only an iPhone each at different locations, can sing a trio and have each person receive the other 2 persons' sound inputs simultaneously while they are themselves singing?
One way is to host a meeting with a service that will record the meeting. At work we use Microsoft teams and that will certainly work, but we pay for this. I believe Zoom will record meetings as well. Latency for close timing will certainly be a challenge - even in professionally managed WiFi and business class Internet, there is often delay that makes it hard to call and response let alone synchronize a trio.
As I mentioned in a clarifying comment, try to test your latency with FaceTime audio group chat over audio. Adding video is fun but can add more latency and time delay. If your networks are fast, record the screen on one device and you’ve got your love setup and a recording.