Tested Квантовый большой топор (and later, Квантовый большой меч) by looting it on live and repeatedly copying the character to the PTR until it could no longer give me new appearances. I have most appearances already. Copying this post onto other pieces as the observations are universal. Here's a rough categorization of the drops I received.

What I Received:

1. Removed by Cataclysm: Old weapons that either no longer drop at all or are .001% drop chances are again obtainable from Quantum items. Examples I received were Тяжелая огрская секира, Волчий топор Черная металлическая секира Боевой топор Злобного Плавника Туннельная кирка
2. Ultra-rare: Received Маятник Рока, one of the rarest items in the game. Also received Неретзек, сосущий кровь, but this was less exciting as it has an easily obtainable shared appearance.
3. Never-Obtainable IDs, Shared Appearance: Received items that have never been obtainable to players. However, they have shared appearances with other items that are obtainable. It is only the item ID itself that is a new unlock. Examples I received were Лабрисса передового бойца Бесподобный дренорский стальной боевой топор Призрачный большой топор Тронутая холодом лабрисса. I received roughly 10 IDs of the weapon titled Бесподобный дренорский стальной боевой топор and Дренорский стальной боевой топор
4. Boring Same Appearance, Different ID: yes, the same as #3 but I want to stress that you can get "screwed" and get a very easily obtainable ID for an appearance you have. Examples are a common weapon from BFD and an axe from Lei Shen. I had these appearances already, just from different items. I also received the timewalking version ID of an axe I already had.
5. Generic New Appearance: to state the obvious for the sake of being thorough - I also received several axes that were not interesting that I was missing such as Shadowlands raid drops.
6. BMAH: I received the Солнечная лютня короля-феникса, which has only ever been available through the Black Market Auction House. Also received Арканитовый потрошитель
7. Tokens and Caches: I also received axes from the Pandaria Heroic Scenario Cache Героический сундук с сокровищами and the Garrison Grandiose Armament tokens Потрясающее оружие.
8. Events: Received Калечащий топор, which was only obtainable during the Wrath of the Lich King Scourge Invasion event. While this also applied to Arcanite Ripper, this is significant as it has not been on the BMAH.
9. One Never-Obtainable Appearance: Мастерски сбалансированный топор is the standout as it is both a unique ID and the only item I received that was 1) previously never-obtainable and 2) present in the game's appearance journal.
10. Island Expeditions - Received Трофейный фараккийский крушитель from the Quantum Greatsword, so island expedition drops are in the pool.
11. Vault? Dinar? - I have not gotten to the bottom of it, but imagine the good folks handling the All The Things community and addon will know the answer: I received 8 IDs of Джайтис Тюремный Клинок. 4 IDs are obviously intuitive as direct drops from the raid, but the other 4 - I do not know what the 4 other IDs come from, although they do correspond to the original 4 raid appearances.

What I did NOT Receive:

1. Vendor Items: ~~I did not get any vendor items. I am missing some Shadowlands anima appearances and did not get these.~~ Yes, the preceding statement is true for my Quantum Greataxe testing. However, Квантовый большой меч testing, my 2nd Quantum drop, brought two contradictions. 1) Меч ученика, a white quality sword sold in several major cities and 2) Кирийский двуручный меч an anima vendor item. Strange that I received one anima vendor item but not others - but the vendor for the Kyrian Greatblade is somewhat unique compared to other vendors.
2. Quest Rewards: I never got around to getting the easily obtainable Большой топор жестокости. I did not receive this or any other quest reward. Even after Квантовый большой меч testing, I have not received a single quest reward.
3. Revamped/Removed Dungeon Drops: As an easy example, Секира могильного камня was removed from the game when Scholomance was revamped - and has been introduced again with 10.1.5 with the return of Old Scholomance. I did not receive this item or any similar item in any capacity after exhausting the Quantum Greataxe token.
4. Appearances Not In the Journal: Yes, I received many never-obtainable IDs - but every appearance was present in the game's built in journal.
5. Dragonflight Items: I did not receive any Dragonflight weapon.
6. Crafted Items: I never received a crafted appearance. While I have every pre-Dragonflight crafted appearance, I do not have every crafted ID.

Other Notes
1. Challenge Modes - The character I am looting these on has completed both MoP and WoD challenge modes and while I seriously doubt the rewards are in the loot pool, I, personally, cannot conclude with objective certainty one way or the other.
2. Corrupted Ashbringer? - No. Квантовый большой меч was my 2nd item to exhaust and no original Naxrammas items were in the loot pool for either the sword or greataxe.
3. Квантовый большой меч- Quantum Greatsword was the 2nd item I received from Deios. The only substantial deviations Sword testing informed over Greataxe testing were 1) Island Expeditions are in the loot pool and 2) Some vendors are in the loot pool.

Комментарий от redlake

Looted this and it added Парные клинки страданий Аландиен to my appearance collection, but in red, not green. Парные клинки страданий Аландиен originally drop off Мал'Ганис (Lords of Dread) in Гробница Предвечных

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