I have not yet received the "Those Held Dear" emblem after watching the stream and claiming it from my Twitch Drop Inventory. My account was connected at the time of claiming and remains so at this time.
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To confirm that the game knows you have claimed it can you (using the app) go to Settings > Redeem a Code. On the new screen tap where it shows Code Redemption with two little up/down arrows. Select Partner Rewards. Does it show Destiny 2 Twitch Drop: Those Held Dear Emblem ? If it does, launch the in game Collections. Flair > Emblems > General. It should be on the third page.