Gleaming Moon is a different perk than Nascent/Ascendant Gleam. Nascent/Ascendant are effectively an elemental resonance bonus, like Pyro/Hydro/Cryo/Geo/Anemo/Electro resonance. There's a different "Gleaming Moon" effect tied to each of the new Nod Krai artifact sets. Each character with a different set is getting a different "Gleaming Moon" buff, which counts toward the artifact set's effect. To be worded a bit more clearly, it should say something like "for each unique Gleaming Moon effect active in the party."
So in a case like Nefer and Lauma, Lauma is wearing the Silken Moon set, which has one Gleaming Moon effect (Gleaming Moon: Devotion), and Nefer is wearing Night of the Sky's Unveiling, which has a different Gleaming Moon effect (Gleaming Moon: Intent). Since there are two unique Gleaming Moon effects active in your party in this case, both Lauma and Nefer are getting 20% Lunar Reaction damage bonus from that clause on their artifact set bonuses. ("All party members' Lunar Reaction DMG is increased by 10% for each different Gleaming Moon effect that party members have. Effects from Gleaming Moon cannot stack.")
If they ever add another set with another unique Gleaming Moon effect, you could get 30% Lunar Reaction damage bonus provided you had all three artifact sets in one team.
For Linnea, in your case, you're probably going to want her on Aubade, Columbina on Silken Moon, and Zibai on Night of the Sky's Unveiling.
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