Just as a note, what you are talking about is not a virus. It is more akin to a parasite, although not necessarily, as a form of resource-stealing from the host is required for a parasite status. Also, great question!
The fact that anyone, everything from your best friend, to the president, to your pet, can be under control of the villain is quite terrifying. But, in a narrative, it might not be so terrifying to the reader. The reason for this is because for a character to be menacing, it needs a "face".
When I say face, I don't actually mean a face. It can be that, of course, and it works well. But in your case, that wont be too easy, as the villain will probably most of the time be inhabiting people, and when it is isn't, it just a wispy cloud.
So, what will your villain's face be then? It can be anything, as long as it is of him. Let me give an example; The movie Bird Box had some of the most terrifying villains in my opinion. And they didn't even have an appearance (at least one that was shown to the audience). So, what was their face of menace? Their effect on the environment.
Whenever someone looked at them, their eyes turned black, and they promptly killed themselves. The first scene when the main character is sitting in the car with her sister, and set sister looks at the "monster", and then kills herself, is perhaps the scariest scene I have seen in my life. Why is this?
Because the sister kills herself. She does perhaps the most drastic thing a human can do to their own body, and she does it because of the villain. She doesn't do it out of her will, the villain makes it her will. And that is scary, because one of the things we humans value highest is our own freedom to do what we chose. To do what we want to. And when what we want to do is suddenly in someone else's hands, that is scary.
So, the face of the Bird Box villain is their ability to make anyone kill themselves just from a glance upon them. Something which helps to this effect is the aesthetic part. They eyes turns black, which is always a chilling sight. Also, their presence is to be experienced. Though they cannot directly hurt any of the characters, their physical impact on the world gives the illusion that they can, the physical impact being wind picking up leaves and moving trees and bushes.
Obviously, since undetectable is key for your villain, you can't really have an aesthetic element to the mind control itself. But if you're able to, try to sneak in something aesthetic. Something left behind, perhaps were the victim was possessed.
As for the face of your villain, from the outside, it looks to be the fact that it can control the minds of whom they possess. That is scary, for the same reasons that the villains are scary in Bird Box. Lack of personal control. So, milk this. Stress it. Implant this scary thought into the reader's mind, and let the fear it generates grow with the progression of the narrative. You can implant this idea with the 3rd-person or 1st-person narration, or with side-characters talking about it in great detail.
Giving your villain a face isn't the only thing needed to make them menacing though. You need to let your reader know of their motivations, and the possible consequences if they win. Possible is key, because knowing exactly what will happen isn't always good. It can work, as with for example Avengers: Infinity War, where we all know what will happen if Thanos snaps his fingers. But keeping some ambiguity to exactly what will happen if the villain wins can be very effective, and it's all because of one thing: the fear of the unknown.
And this is perhaps the biggest strength you will have when you're establishing your villain. People have strong imaginations, and because of this, any danger that is unknown turns on the anxiety parts of the brain that start creating all these different kinds of scary possibilities. Because you can't see your villain. Your villain exists inside people, and so the reader can only "see" the villain's actions, and the consequences thereafter.
Other than that, it is the interactions between characters and the villain that builds up their scariness. As they are inside people and probably want to stay undetected, this becomes a little tricky. But you can make it work. Have the villain visit characters in their dreams, or talk to them via telepathy. Or maybe have a character talk to a possessed person, before either that person is disposed of or the character is killed, as a result of the cover being blown.
The bottom line is, if you're creative and actively think about what is scary, then you'll intuitively make your villain scary using good and refreshing methods. That is what is most important.