As have many others, I completed the Contest Mode version of the Vow of the Disciple raid during the extension period and have yet to receive the emblem, or even the in-game pop up in relation to the emblem's distribution. All characters have been loaded daily and had their post master checked, their collections and triumphs checked, etc. I have even gone so far as to uninstall and reinstall the game, though I never suspected that would have an effect on the current situation.
My in game name is Hutch#6313
Bungie profile: https://www.bungie.net/7/en/User/Profile/254/4106659?bgn=Hutch
Platform: Steam
Raid report of the contest run: https://raid.report/pgcr/10346436497
Several of my teammates for the run have had their emblems delivered already.
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I'm also awaiting the emblem