So Taric never ascended Mt. Targon like the others?

Yea it almost certain that he is from Targon but that doesn't necessarily mean his love for Gems is changed.

Well, Targon is "connected" to other worlds besides Runeterra so I'm sure Taric's story will be influenced by this somehow, kind of like a nod to his previous otherworldly origins.

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As of now, Taric and Zilean come from their own special lands unrelated to any other lore in Runeterra. But I don't expect that to last. Riot changes the lore at a concerningly high rate. I'm almost sure Taric will have a different back story once he gets his update.

Actually Zilean's country is still sorta canon. It was on the Map of SHURIMA! Iirc

Its not so much that they are change the lore t a concerningly high rate, as they scrapped the old lore around the Freljord event. They just haven't yet caught up with the implications. Effectively Taric doesn't currently exist in their narrative, nor do a lot of other champs who haven't had events/reworks happen involving them yet. Most of them are going to remain relatively unchanged, though others like will end up with entirely new lore, Taric just happens to belong to the latter.

Urtistan (Zilean's old city of origin) was always situated in Valoran, near Shurima. It's true that a lot about it could probably change once Riot decides to flesh it out more down the line, but Vel'Koz apparently paid a visit to the ruins of Urtistan, so it's still a thing in the present canon.