They come out of nowhere, and disappear just as fast, leaving a trail of destruction in their wake.
However, whenever a human is attacked by a phantom and manages to fend them off and survive...they have a chance to gain superpowers from this. This is where our protagonist gets their powers from. I also figured out the power I wanted the protagonist, who I decided--hero and villain alike--adapts the name Projection, which amounts to a specific form of 'ultimate illusion'.
In the area of about that of a house, the protagonist can flood an area in an energy, manipulating this energy to their will, but this energy is, explicitly, defined as an 'illusion'. But it's an illusion that is so, so strong as to be a local reality warp of sorts; nothing is immune to being affected by the illusion as if it were real. But the illusions can't be detected, because they technically don't exist, giving Projection a great ability to hide well.
This energy allows Projection to wrap themselves in an energy suit of sort, allowing for no need for a costume; the powers act as the costume. These illusions are absolute; nothing can break them. True sight cannot penetrate them, no sense or super sense can penetrate them, they are absolute, existing as both real and yet, not real at the same time, able to affect the environment without any true counter.
This energy cannot take the form of constructs, a la hard light. It can be manipulated in size, shape, exact form, color, and such, but mostly, it has the effect of multiple elemental powers. The energy can make energy beams, a la light beams, lightning bolts; the energy can burn; the energy can slice like wind or push like wind; it radiates as an aura of the color Projection chooses (yellow as a hero, black as a villain), and has these sorts of effects.
I chose this as the power because it needed to be a power that worked as both a hero and villain power, which was tremendously strong, but not godly strong. A power with set rules and limitations that prevent it from doing anything, yet versatile enough to allow it to do most things.
In this case, Projection has what amounts to flight by surrounding the energy around themselves and then elevating the energy off the ground, and similarly so, what amounts to a flash-step: not proper superspeed and not proper teleportation, where Projection will rapidly move from the center of their energy field to the edge of their energy field, but then has to wait for the energy to catch up before pulling this stunt again, so to speak.
The effects of the energy last after the illusion has passed. A destroyed camera will remain destroyed. Surveillance footage won't be able to make out what Projection looks like underneath their powers once the illusion is dispelled. So for all intents and purposes, the energy field is 'real', but the powers being, explicitly, illusions, give Projection the protection of their powers being undetectable, because their power while having the absolute true effect of being real, technically doesn't exist.
Because these energy illusions can't take the form of constructs, no god-like creating something out of nothing. (That, plus the limited range and the fact that it's not real and thus will disappear.) No mass-cloning, no mass creation of objects. Just a limited ability to use concussive energy, piercing energy, redirecting energy, etc.
It feels like exactly the power I need and I love it and feel like I can actually make something out of it.