I picked up the Ritual Initiation quest from the Emissary (along with the one that gives the shiny Liminal Vigil), as did my other fireteam members, then we completed a run of Spire on Eternity mode. One of the other guys had his quest complete normally, and he picked up the Navigator as a reward, I'm not sure about the other one and they're currently asleep so I can't ask, but I was not given an option to pick up any rewards from the Emissary aside from the shiny sidearm. I can't provide any screenshots or anything, because the quest also isn't present in my quest log anymore despite not giving me anything.