Seems to me the debt would be tied more to having less of your soul to work with, and whatever you think the consequences of that might be.
For Harry, this initially expressed as a numb hand when he did a hand-force-evothaum, and likely also in a desire to do more "soul regenerating" stuff, as in his relationship with Luccio.
In a lot of ways Soulfire in the books is skinned as a lesser form of the death curse. You could skin that as being more likely to be ruled by your aspects, but Harry seems to see it as something that risks his life in a way similar to how firing your memories of fire at people as a ghost is risky. After the first book he's more careful with it, so we don't tend to see him piling up "soulfire" debt. If I was playing a soulfire based character, I'd likely go down the road of debt being consequences of an incomplete or damaged soul, and think about what using certain kinds of magic would translate into.
Harry mostly uses soulfire with his fire spells, primarily to beat the catch on critters vulnerable to faith. This use seems mostly to make him more aggressive or inclined to gloat/victory dance (think about how he behaved in Changes when chasing the vampires in the first scene). This might be because he tends to throw fear/rage at enemies with fire, and with less of that in his system he behaves more like a fight is a game or contest. When he made a hand construct, his hand went numb, which is pretty obvious. When he's used it to reinforce defensive spells I've not noticed anything in particular, but maybe Jim's doing something subtle or I'm off base entirely
Mostly though I think Harry got a lot more careful when he realized he's throwing his soul at people so he hasn't been getting into a lot of situations where he incurs debt to it as a solution.