Speaking as a voice consultant, I distinguish between 'voice quality' and 'voice use'.
Voice quality is the sound or timbre of a person's voice: raspy, breathy, nasal, etc - which is a product of how a person combines the 3 things needed to produce a vocal sound: breathing, the sound source and resonators/articulators.
Voice use is the amount of vocal variety they use. Voice use includes volume, speed, pitch, timing (pauses) and emotional tone. As you say, this is totally different to accent. or voice quality.
Idiolect includes individual uses of words and individually-favoured ways of pronouncing certain words, or preferences for particular patterns of speech.
Accent and dialect come under cultural or regional aspects of language which embrace all of the above.
If you're looking for markers of personality in voice, they'll more likely be found in the voice-based categories; social status will be more the other, accent-based ones. These kinds of associations should be treated with caution.