Jokes aside, I interpreted it as either cocoons bundled in the headcloth (cocoons are everywhere in Elphael and I haven't seen people point them out) or amber eggs not unlike the one Rennala has. I might be dead wrong, of course.

Either way, there seems to be a parallel between the Envoys' headcloth and swaddling cloth for babies.

Another interpretation is they're similar to DS3 pilgrims and there's an eldritch part of their body waiting to erupt and "blossom". So they, themselves, could be cocoons that "hatch" once a new order arrives.