I can't seem to get a consistent answer regarding the question of whether or not satellites (moons) of trans-Neptunian objects are considered to be trans-Neptunian objects, given that they do not orbit the sun directly. Any help clarifying this issue would be greatly appreciated.
Yes/No as needed.
The MPC, which is fairly authoritative, lists only (134340) Pluto, and doesn't include Charon and the other satellites of Pluto. Formally, binary asteroids are given a single classification, so 2000 CF105 only has a single code, despite being formed of two pieces of ice and rock.
In other contexts it might be convenient to include it. It wouldn't be wrong to include Charon in a discussion of the formation of TNOs.
Nobody really cares enough to try to pass any kind of rule, it is normal and acceptable for context to establish meaning. Language exists to serve us, an not the other way round.