The Core set isn’t legal in the current Twist season. However,
There are more examples in that topic, namely Ship’s Chirurgeon and Acolyte of Pain, but I suppose the list could go on.
There used to be other old issues with Twist and various card sets: Caverns of time not usable in twist — but this is different, and you cannot even see a consistent pattern.
Hopefully this gets fixed soon. I reported this bug myself over a week ago, before the recent patch, but no fix so far
Oh! You mean that: (Twist) Some Core Set cards missing?
The title seemed so confusing to me that I must have missed it while searching for existing topics.
Having read it, I can say that your account isn’t completely accurate or exhaustive, according to my findings reported above. Nevertheless, thank your for your feedback and confirming the bug!
You can use core set cards that are also cards from other legal sets of the mode
Ships chirurgeon is also a CoT card
Acolyte of pain is also a legacy card
Have you even read the reports or understood the issue before trying to play the explainer (again)? 
Dreadfully sorry for being a bit snide, but you really sounded like a Derpan with this particular comment — nothing personal. 
They’re saying that some core cards aren’t usable when they should be, for example Raven Idol.
Well I did read what was written in here but I may have it gotten it mixed up and understood the other way around
[Hearthstone] Fixed an issue where certain Legacy cards were not included in the eligible Twist Wonders card pools.
Dunno if this is related, but one might look into it… once the patch goes live, that is.
By the way, I had another theory that they forgot to update some internal card pool (they do use such things sometimes, like the ‘Core reserve’ [1], for example) for eligible Twist cards in accordance with the Core set rotation (the previous iteration of ‘Wonders’ was in the Year of the Wolf [2]), but it doesn’t seem to add up, either.
Maybe they don’t know what they’re doing themselves and/or have given up on the mode altogether.
[1] https://hearthstone.wiki.gg/wiki/Core_reserve
[2] https://hearthstone.wiki.gg/wiki/Twist_format#Formats