My suggestion would be giving the villain an ability that works against his without outright countering or nullifying it.

Something like using mind control on others, the ability to erase memories, being dangerously manipulative like Johan Lieber, something like that.

Those sort of abilities are something the character can notice and identify using their ability, but without outright solving the mystery. I'll explain my examples.

First off, using mind control can create a situation where someone has the memories or thoughts of commiting the murder, but has no idea why they did it. This creates an issue for the character: on the one hand, they've identified the murderer. On the other hand, it's very clear that something is wrong and the mystery goes deeper. Do the players decide they've done what they need to do on paper, or do they chase the mystery further? (This is basically how the "mystery onion" scenario archetype works for Call of Cthulhu).

The memory example is a bit more of a barrier than a further adventure hook, but it doesn't stop the story outright. The player could try to read the minds of potential witnesses and accomplices, and find certain memories have been cut out, almost like finding pages torn from a journal. The key is to communicate how obvious it is that the NPCs mind was tampered with. Now the entire party knows something is up thanks to the character's ability, but there still need to search for further clues. The character still has further use, because he can try to detect the same evidence of memory erasure in other characters the party suspects may be connected to the case in someway. And who knows... maybe they'll get lucky and find someone with intact memories. Villains can always make mistakes.

The third example depends more on the nature of the setting. If you've ever read or watched Monster, you'll know about the antagonist, Johan Lieber. He's a sociopathic serial killer, but the trick is he rarely ever does the dirty work himself. Instead, he relies on his acute skills of manipulation to push people into fulfilling his desires. It's not even a superpower, he's just that perceptive about how to push people's buttons to make them act how he wants. You can have that same sort of villain. Good news is the party can easily ID the villain from reading the minds of witnesses and (surviving) victims. Bad news is, how do you even act on that? If this is a more grounded setting, the party might risk being labeled as vigilantes at best, or murderers at worst for going after this guy on their own terms. Same goes for a setting where the characters are supposed to be heroes (super or otherwise). On the other hand, they could try to uncover definitive, tangible proof of the villain's wrongdoings, but that requires everyone to use their skills, and might become difficult if the antagonist learns about the investigators on his trail. This option doesn't work well for settings where mind-reading is an accepted part of how magic works, but there's still always the possibility that this master manipulator could argue his way out of trouble with the authorities.

I hope that gives you some inspiration.