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.

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.