That trope always throws me for a loop because it's one of those fanfic-only concepts that feels like it's been around forever, but if you think about the original canon, it makes zero sense—which is kind of what makes it fun to explore. Writers have to bend over backwards to make it plausible, and honestly, the methods they come up with tell you more about the story they want to tell than about 'Harry Potter' itself. You see a lot of magical lineage tests, which are basically a get-out-of-jail-free card for any secret parentage plot. Some ancient artifact, a goblin-forged contract, or a spell at Gringotts that reveals true ancestry gets trotted out, and boom, instant drama. But the lazy versions just have her sensing it through the Dark Mark or some vague 'magical resonance,' which always feels weak to me.
I'm more interested in the slow-burn psychological reveals, where Bellatrix pieces it together herself. Maybe she's captured Harry or is obsessively studying him post-Department of Mysteries, and she notices his eyes aren't just Lily's—they're her own mother's eyes, or he has a specific Black family mannerism. Or perhaps she finds a shredded memory in a pensieve, a hidden letter from Voldemort or even Sirius hinting at a switch at birth. Those stories often hinge on Bellatrix's own madness making her the only one who could believe such an outlandish thing, which adds a tragic layer. The reveal isn't just a fact; it becomes part of her fractured reality, and that's where the character exploration gets messy and compelling. The plot device itself is just a doorway into how Bellatrix would actually react—would she try to 'save' him, would she see him as the ultimate prize for the Dark Lord, or would her hatred for the 'half-blood' override any maternal pull? I've read one where she tried to 'purify' him with dark rituals, which was horrifying but oddly in character.
Ultimately, the 'how' is less important than the 'why' the author chose it. A quick blood test means the story is about the aftermath. A slow, painful deduction means it's about Bellatrix's mind. Either way, it's a vehicle for exploring two characters who, in the books, share nothing but mutual loathing, and that contrast is the whole appeal.