All the Cults have their own version of that story and they all just so happen to paint their preferred God in a great light. The Taalites say that Taal led the charge, the Verenans say that Verena was the only one that believed Ulric when Ulric was going around saying the demons were coming, the Asur say that Asuryan was the first to fight against the demons and the first to fall, and His eventual rebirth is what won the war. Like with studying IRL historical accounts, despite all the clear biases if you read enough you start to see the common threads between them that give you an idea of the truth of the matter. The growing threat, the widespread disbelief, the few believers talk around those on the fence, the long war, the final stand before a deus ex machina saves the day. All of this can be mapped to the historical timeline given by the Elven and Lizardmen histories with reasonable accuracy - the Gates begin to fail, they fail completely and demons are unleashed, the Lizardmen bear the brunt of the attacks early on, daemons become a worldwide threat and are opposed by the Elves and Dwarves, the Vortex turns on and the Daemons are banished.
Where it gets weird is what isn't converted into the vocabulary of the ones telling the story. A Taalite legend from the Obernarn Stone speaks vaguely and darkly about 'immortals', possibly the Old Ones, but speak of the Chaos Gods as four of them, which, what? It also has oddities among Taalite's allies: Margileo, a very minor God with a weirdly non-Reikspielish name with just a handful of worshippers in Averland, as well as Sotek the Snake (???), and it gives credit for the final victory to what is almost certain to be Asuryan. The Grey Order's myth adopted from the Asur says that King Taal inherited rule of the world from Asuryan after Asuryan was slain by Chaos, which doesn't fit Asur beliefs about Asuryan and Kurnous, nor does it fit Taalite beliefs about Taal, and for some reason it also name-drops Tlanxla, which is the name of a Lustrian Temple-City that's been in ruins since the Coming of Chaos. The Ulrican legend Codex cites has the same sort of oddness: it should date back to a time when he was the primary God of the Teutogens and the other Gods were either that of other pre-Imperial Tribes or of distant Tilea, and this is kind of supported by Ulric being described as 'prince of ice and snow' with no wolf associations (which were believed to have come about after the Cult of Ulric absorbed the Cult of Lupus) - but he is also said to be the younger brother of Taal, which is... odd. Maybe it's from a time when the seasonal trinity worship of Taal/Rhya/Ulric was splitting into three distinct deities, but while that would explain why Ulric is given second billing in an Ulrican legend, that process should have been long complete by the time the Southern Gods became known to the Teutogens.
It all seems like a jumble of syncretism, mistranslations and cultural misunderstandings, but you can't dismiss it entirely as a source because things come through that have no reason to be known by the ones doing the telling. Why does an ancient human Runestone have a cameo from a Skink God whose entire deal is that the Slann keep saying "who the fuck is this guy, he's not in any of our writings?" Why does it have a very clear description of Asuryan? Why does an Ulrican myth include beliefs from points on the evolution of the Cult of Ulric millennia apart? Or more explicitly, how does a supposedly ancient and unsourced Ulrican myth manage to supply a very neat 'just so' story to the evolution of Ulric's depictions by his worshippers, a process that took thousands of years, most of it long before any written records existed and unknown to modern scholars? Why does an Asur myth have Tlanxla, who may have been a Lizardman Sky God of some sort but is obscure enough that even those that have access to the wiki only know of the city named after them, as a sword wielded by the Daemon Ulgu? All these mythologies that should have been separated by oceans and millennia keep describing the same events and beings with too much accuracy and too often to be coincidence. The only conclusion that makes sense is that these are the same events being seen through different cultural lenses.