I been thinking...
Fuck the whole lazy-ass "satellite" explanation. The only way Fallout76 could have Brotherhood power armor a hundred-odd years before the Brotherhood even got to the east coast is if FO76 is one of the many simulations designed and run by Dr. Stanislaus Braun in Vault 112. He would have to still be alive and aware of the Brotherhood, so FO76 would have to take place just before the events of FO3. It would also explain some of the features of FO76 gameplay - namely the lack of NPCs, magical respawning, and omniscience with regard to other players' positions.
This does not excuse Bethesda its wanton disregard for lore. You hear me, Todd, you fucking closet hipster scumbag?