The creators hoped no such thing, magic is not part of this story in any way. The last time the world had magic was thousands of years before when the children of the forest still existed and the white walkers first showed up.
If that’s what had been established in the first show (Game of Thrones, I mean, not the first episode of House of the Dragon), then, sure–the creators can make whatever rules they wish. But instead, they tied the presence or absence of magic to the presence of living dragons.
(If the books say something different, then that’s fine, too. I’m just talking about the shows, though: not the books.)
As far as I remember, only one character says anything about that - the warlock in the House of the Undying. He says that his powers grew after the dragons were born but how does he know that? It could have been a consequence of the White Walkers waking up, which he does not know about. He just picked the “supernatural” thing he does know about to account for it. And use as an excuse to take the dragons. At that point, the Faceless men had been doing their thing at the House of Black and White for centuries. Melisandre had been alive through her magic necklace for a few hundred years. Unless some other characters talked about this, I’d say we can’t really know that living dragons affected magic and aren’t just part of magic ramping up to kill the Night King.
Maybe if the storyline follows Rhaena and the kids in Pentos we will see some of the magic. Maybe we will see an actually young Melisandre. But this story is focused in Westeros where the magic is apparently not so obvious or discussed.
That would be interesting!