"Continuing the story of the game" isn't the same as continuing the major arc it's been running on since 1.0. The only plot points derived from the Ancients not 100% concluded by the close of Endwalker is the cosmic order put in place by Hydaelyn, a couple of loose Ascian reincarnates running around, and Garlemald's political position. The first can't really be resolved, the second is implied to be a nonissue by 6.0's closing scene, and the third won't be resolved until the Reconstruction content they're obviously planning (or will be forced to implement due to player demand) is completed and the "Ilsabard Expansion" happens (because they wouldn't leave that much story potential just hanging there).
Other than the few (plausible) remaining Ascians, nothing linked to the Ancients is really left. The two Eldest Primals are dead. Zodiark's fragments on the other reflections disintegrated with his death (except the Thirteenth's, which was through a long process only possible thanks to the Void's lack of a Lifestream transfigured into Zeromus, then sealed into a Memoria crystal planted out in the First's Empty). Most (if not all) of Zodiark's servants are dead. All of Hydaelyn's servants (i.e. the Twelve) are dead. Humanity has proved it can stand on its own two feet and no longer needs the protection or guidance of "gods;" to go back to the Ancient / Ascian well would kind of be regressing on this stance and invalidate the message of Endwalker (succinctly, "forge ahead") by bringing back an element from the past whose story was for all intents and purposes concluded.
I wouldn't say the end of Pandaemonium was a tease for Ultima. She's been done and dusted since the conclusion of Return to Ivalice back in 4.5; the primary point of bringing her up in Pandaemonium was to resolve the Heart of Sabik plot point which had been dangling around since 2.0. Its JP name is actually "Black Auracite Sabik" and it was identified as auracite during the Sorrow of Werlyt questline, but people still demanded more answers and had been doing so for a decade. By including it there people would finally shut up about it - and you can tell it was kind of shoehorned in by the fact Lahabrea makes it clear in no uncertain terms Athena's methods and motivations would be no different had she never found it.
Is it possible Solution Nine will have some link to the Ancients / Ascians? Yes, but I don't want it to on account of their story arc having concluded and going back to them (or their proxies) for MSQ content would kind of defeat the purpose of having done so.