Those two would be the minimum requirements for me. Whether they were released in the way intended isn’t as important imo, because say miscuts should also be discarded at quality control and not be released to the public and I doubt anyone would argue those are not authentic. So imo if a card was created at the same factory with the same process and materials as others and the authorization of TPC/TPCi that would count as authentic to me.
Any card that wasn’t created by the license holders of the IP is illegitimate to me.
Distribution doesn’t matter to me. I don’t care what was intended. I only care that the card was printed in a factory that was licensed to create it when said license was active.
If 20 years later an old printer was fired up by the same company using the same hardware and files then it’s a reprint. To the extent that matters is open to interpretation, but I would never want such a card if it was being passed off as original.
Imo, the points you mentioned refer more to ‘official release’ vs ‘unofficial release’, which is different than ‘authentic’ vs ‘unauthentic’.
I agree with @squirtle1000 above, that if they were printed by the license holders; in the correct time-frame; and in the intended factories, they’re authentic.
In your second list of examples, that would mean almost all are authentic, except for:
The COLLECTOR-stamped Charizard (unofficial stamp on a real TCG card)
the prototype cards, usually printed on regular card-board and primarily only used as printing tests or playtests
Only those two categories I’d say are neither official nor authentic, and I can understand grading companies nor collectors wanting them - even though I still think both are cool and will collect both with every opportunity.
All the other cards in your example I’d say are all authentic:
The Akabane’s & pkonno’s closet trophy cards and extra Art Academy copies are just extra left-over copies of real cards.
Complete sets awarded to tournament winners and employees are just regular (Mint) cards, and also just extra copies given for various reasons.
The 25th anniversary Creatures Deck and Ishihara GX are real TCG cards given to TPC employees and illustrators
The Sample Pikachu and other promotional cards that were leaked from events (another example are the Trainer Deck A/B demo cards) are also real cards intended to be shown to the public. Therefore authentic, although not an official release but a leaked (pre)release instead.
And, imho, since 1 and 2 can’t be distinguished from the official releases (minus some exceptions, like given Trophy cards having the winner names vs extra copies lacking those names), I’d say those are both authentic and official, despite this unofficial release behind the scenes for these specific copies.
Technically everything is “authentic”, but I think a bigger picture is “who” has produced “what” product matters most, and is that entity affiliated with or TPCI themselves, or whatever the topic is at hand one is referring to.
I don’t want to get too deep into Collector Charizard Discourse™, but I will note that this is incorrect.
Collector Charizard’s stamp was applied in a manner consistent with how other officially-acknowledged stamped cards are done. In certain cases stamped cards are actually not done by TPCi themselves, it’s another company that does the stamping. However, random members of the public can’t just go to this company and get them to stamp your Pokemon cards. If you compare the Collector Charizard stamp style and font to other officially-acknowledged stamped cards, you’ll see it’s the same.