What do we call a group of people singing together like this?

A choir is correct because that's the word for a group of people singing together, often in different parts at the same time, so their voices blend into one rich, layered sound.

An orchestra is a group playing instruments, not singing, and a band usually mixes instruments too, often with just one or a few singers — neither is a large group singing together the way a choir is.

Choirs often split into different voice types, like high and low singers, so several different melodies happen at once yet still sound beautifully connected.