I have already completed sleepytime ensemble and have received sleepy emote before. When I received part of that ensemble as a daily gift (duplicate, see screenshot 2), I saw that I received the emote again (screenshot 1) and when I went to the emotes page I saw that sleepy emote had a "new" label on it (no screenshot unfortunately).
1. Have sleepytime ensemble completed
2. Get lucky and receive part of the same ensemble as daily gift (maybe it works with weaving or buying it as well, I haven't tested it)
3.Go to the item collection and see that you received the ensemble emote again