When singing davening in minyan as part of davening sometimes people repeat words as part of the song. What is Halacha on the repeating if it’s not that way in siddur?

One shouldn't repeat words during davening, unless it's in piyutim like Lecha Dodi or Yigdal, where it's not in the middle of brachot, and it's basically just singing, but even then, one should definitely not repeat God's Name. Nevertheless, it's the rabbi who should be the one who corrects the chazan and community, and the Aruch HaShulchan just adds here that it's important to stay away from arguing which is very bad.