Is that power source something internal to their being or something external, as in the case of Squire of Porthos?
I'm going to say that the Q are Boltzmann brains that developed sentience ln/on the surface of the cosmological horizon. They really are the empyrean incarnate. From the wiki:
Holographic theory suggests that the entire universe
can be seen as a two-dimensional
information structure "painted" on the cosmological horizon
The Q operate in the reverse. They live on the brane and project inward to 3D.
I'm going to call that their tidal pool. They exist as patterns. Imagine if you will the dyson sphere from relics, but with the world spanning abhoth creature from solaris on the inside surface, and how that pattern interacts leave a virtual image towards the center (3d space) A higher dimensional version of that--a living brane brain. That is what the Q are.