Base Abilities:

Enhanced physical- Nanomachines and dreams, son.

Mantle of Unconquerable Sun- This power "unifies" things physically. It causes all effects to be shared across things equally. The "Mirror of Conquered Force" spell allows her to change the orientation of force being shared, but requires her to make physical motions demonstrating the turn.

Circle of Harmonious Will- This power "unifies" things mentally. On sentient (and willing) targets, this allows telepathy between Miyu and the rest of the network. This also works on non-sentient targets such as, air, dust, water, earth, space, allowing Miyu to sense their presense, location, and status. Miyu can cast spells across things/people unified by this power.

Cloak of Fleeting Shadow- This power "separates" things physically. Causes them to avoid each other, passing by each other with no friction. This normally can only cause things that are not attached to avoid each other but the "Traitor's Blade" spell can create an edge that cause things (or people) to separate where they were not meant to be separate.

Combined Effects:

Reach of Green Dawn- (Mantle and Circle)
This spell unifies the edge of her weapon with the material next to her target, allowing her to strike at any range, with the requirement that Miyu's weapon has to strike the target from the perspective of her eyes. This specifically doesn't work with Traitor's Blade.

Loom of Stolen Thread- (Mirror and Circle)
This power passively steals the energy of things moving within her Circle, that she can then use. Basically works as Mirror, but passively and with far less dramatic effect.

Edge of Red Dusk- (Circle and Cloak)
This power unifies her nervous system, her reaction time becomes instant. And by also separating the air in front of her body, Miyu can safely travel very quickly, without worrying of splatting against a wall or burning up.

Body of Unyielding Soul-(Mantle and Cloak)
This spell separates her soul from that plane of existence and onto the mortal plane, and then unifies it into her body. Miyu can replace destroyed parts of her body with her soul (which is significantly stronger than even her nanomachine enhanced body), allowing her to continue fighting regardless of any non-soul destroying injury, including complete annhilation. However, by putting her soul on the physical plane, that allows ordinary physical attacks to destroy her soul.

Spell vs Power
Power is innate thing that takes as much concentration as say, moving.
Spell is a focused thing that takes as much concentration as say, doing math in your head, and generally has a drawback or limitation in order to grant a Power a new ability or application.