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To use storage on Xbox you have to drop the item first, the item may not show up on the nearby menu so you might have to pick it up and drop it constantly. When it pops up in the nearby you can then store it, it seems like storage has a 24 weight capacity

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over 4 years ago - /u/MoltonMontro - Direct link

You're playing the game through the Xbox Insider Beta. Feedback should only be posted through there. It's not going to be seen by relevant people anywhere else.

That being said, this doesn't sound like a bug, just a user error and a misunderstanding with how to interact with storage. (Both placed storage, and inventory space provided by clothing).