If you rewatch the scene, you'll notice that the flow of magic is going from the coven towards Agatha, even before she takes control and pulls their magic into her. That implies that they weren't trying to draw hers out, but rather that they were attacking her with some spell. Indeed, it appears as though she's being burned from the inside out, which makes a certain kind of sense, given the stake to which she was bound.
Spoiler:
Yeah. Notably, she only reclaims her own power, rather than stripping Agatha's from her (which would kill her, as it did the coven and would have done to America Chavez in the movie).
It's been shown that people can be saved from the DarkHold's corruption if they stop reading from it, though. The movie even gives us evidence that at least one other Strange has done so. Who's to say that Defender Strange wasn't in a similar situation in the past?
Also, as an aside: rewatching the end of WandaVision just made me realize that they telegraphed her corruption even more than I had noticed. I mean, Agatha literally foreshadows what's going to happen:
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And then the final line, with the illustration of the Scarlet Witch in the DarkHold making way to show Wanda in the background in the same spot.
Spoiler:
Wanda tries to deny it at the time, but by the end of WandaVision, she's fully on that path, embracing her Scarlet Witch persona and reading from the DarkHold. And yet people still want to say: "We didn't see this corruption coming! How did this happen?!"