It's not a software problem: packet round trips are just too slow for singing. A good ping time in gaming is 15ms to the gaming server, achievable with good internet and a wired connection. Double that, because both you and the other singer needs to talk to the central server and we're at 30ms. Then if your system is using 128-sample buffers at 44.1kHz (tight but doable) there's ~3ms each for ADC on your end, DAC on their end, ADC on their end, and DAC on your end, which adds another 12ms. This best case is a total of 42ms, which is still too high.

Singing rounds does work, though, and https://www.cockos.com/ninjam/ is an open source tool for it. You could also imagine some sort of bucket brigade approach for larger groups (https://www.jefftk.com/p/series-singing) but I don't know of any implementations.

Really old style circuit switched landlines get down to the speed of electricity in copper (~0.7c https://en.wikipedia.org/wiki/Velocity_factor#Typical_veloci...) over the distance (to your local exchange and then to your neighbor) which would be fast enough if you lived nearby (c is l ms per mile). But today it's all packet switched which adds latency in exchange for much higher capacity.