I'd say the Old Ones of fantasy share the same real-life origin as their 40K counterparts simple because 40K started with a lot of fantasy's "genes" in them. Here's my take from my efforts to compile (and make sense of the timeline with the least alteration to the official materials as possible).
So in the 1th edition WFRP rulebook (released 1986), the polar gates were already in place and the Old Ones were the "Old Slanns", and Lizardmen
were supposed to be the degenerative desendants of the Old Slanns themselves, their technology and knowledge lost and retained only as dogmatic rituals. Some creatures of the void -- which were to become "demon and deities in a world deprived of the protection of the old slann" (p263.). The degenerative Slanns (what lizardmen were called) managed to bound some of the less malicious warp entities to their cause, which became their gods.
The warp entities were also largely benign enough, or at least not entirely malicious, with two opposing factions on the extremes: Chaos and Order. The Gods of Law lost the Kaoskampf at the beginning, leading to a Chaos domination over the world.
I write the above because in my forrays to compile my own list, I've come to find such information isn't so much abandoned in later editions, merely transformed. The timeline of the world in both 3rd edition WHFB and the 1ed WFRP actually match up to the modern timelines with errors of about a couple years.
In WFRP 1e, it is also stated that the Old Slanns had already travelled across multiple stars, and learnt of the threat of Chaos well before their arrival on the planet of Warhammer Fantasy. They came to this world with a purpose, transplanting alien creatures and seemingly tinkering with genetic of the local fauna with some indescript purpose (263). It's clear their uplifting of the Elves, Dwarfs, and other races were kept in subsequent publications by GW alluding to this fact.
This IMO is also inherited by 40K as the Old Ones in that setting also created multiple races for war, but this time against the Necrons. Given in passed books such as the Realm of Chaos supplements and background books like the Liber Chaotica, where chainswords were a chaos gift in both fantasy games, it was implied the two settings were connected somehow. It is therefore my speculation that, the planet of Warhammer Fantasy had been one of the Old Ones' many laboratory worlds where upon they experimented to create new warrior species or improve upon existing ones (such as Eldar/Elves) -- this, however, does not explain how the Dwarfs, Halfling and Ogres are created by the Old Ones here but in 40K they are subhumans that came about during the Long Night.
The only info I know of this is from the WRFP 4th edition supplement Lustria, in which the location known as Mirror Pool of Tepok is expanded upon, said to be guarded by a Coatl and is speculated by Skinks to have connection to another dimension in which the Old Ones dwelled.
There's also the the Sentinels of Xeti, which are a bunch of obselisks what apparently acted as radio arrays, as one skink priest claimed to have heard voice of the Old Ones from it (the Slanns denied this).
So there's a possiblity the Old Ones still exist, somewhere, in the galaxy, just in hidding.
I think the interesting question here is whether the Old Ones were the same gods of the Elves, Dwarfs, Humans etc., in different guises. In 7th edition WHFB Lizardmen army book, it is stated that the Lizardmen dieties were names extracted from sacred plaques that the species come to believe to be gods (p36). No living Lizardman have first hand experience with the an Old One -- not even the five second spawning Slanns, to which Lord Mazdamundi belong, met the Old Ones (p17.) Thus, it's far more, IMO, likely that the Old One dieties the Lizardmen worship are warp entities that represent the aspects of the Old Ones the Lizardmen attribute to and come to be transformed into their gods.
The Elven pantheon, on the other hand, has had multiple extrapolations in WFRP2E and 4E as to whether they are the same as the Old Ones; of course, IRCC, one high elf Archmage denies this, but I think of it more as they have their own interpretations of the Old Ones, which they likely had some interactions with before the polar gates' collapse and come to worship these ideas as their gods.
One important point I put forward is how these gods can have their avatars, such as Ariel and Orion, in the physical world, who have some permanent connection to Isha and Kurnous, apparently. It indicates to me that these gods such as Khaine, Asuryan, Ulric etc. are warp entities that connect to the psyche of a living being. This would also work in 40K as the Fall of the Eldar saw the Eldar gods killed within the Warp ("War in Heaven"), thus necessitating their status as warp creatures.
WHFB 3E has one depiction of two Lizardmen, one Elf, one Dwarf, and one female humanoid (unclear if elf or human) in WHFB 2nd bestiary p10. There are some elsewhere who assume them to be the Old Ones, imply they were a group of different species. Detractors believe it's just artist depiction.
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