Claiming Season set gear on a season alt

I have completed Season 21 on a Necromancer and gotten to 4/10 in Slayer on the Season Journey. I got my 6 pieces of set gear on the main, via the mail as per usual.

I then re-birthed a Monk as a season alt, and he's now 70. In the Season Journey screen it tells me that I have unlocked the set pieces, and they have been added to my collection.

Are the Monk season 21 set pieces in a super secret hidden place where I can just go and collect them? Or is there a bug in the Season Journey screen where if you roll a season alt and get to 70 it will always show that class' season gear as unlocked?

Image below shows the Season Journey page for the Monk alt.

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The Season Journey is shared across your account. Haedrig's Gift can only be claimed once per season, not once per seasonal character. It wouldn't personally call this a "bug" per se; I'd call it a design oversight, but that could be argued either way. Regardless, the UI could be more explicit, and is arguably lying to you in this case.