"Paraconsistent logic" by no means points out any particular logic: There are a lot of logics that are called paraconsistent because they have models refuting ex falso. But I've yet to see one that was useful for anything or illuminated anything about truth.
There are a lot of useless formal logics out there.
My own view on truth exists very far from but in the same space as logic. I don't think a formal truth can exist as a singleton, but that one must consider the set of all statements together with all possible truths. Maybe this is a matrix of statements times the transpose of statements but I'm not sure about that implementation. Anyway, you get an immensely sparse product where statements match up with everything that is true about those statements, along with everything that is false about those statements. You can then attempt to compress this data and that compression is the logic. The vast sparseness, meaning much more false evaluations than true ones, implies a lot of structure which can be exploited in compression.
I don't think anything but many-valued logic like this can be consistent.
There are a lot of useless formal logics out there.