Distinguish proof mode from unsat core mode (#8062)

Distinguish proof mode from unsat core mode (#8062)

Previously, we were making unsat cores mode the source of our configuration for unsat cores and proofs at the same time.

This led to a lot of unnecessary complication in the logic, and would allow bugs e.g. if produce-difficulty but not produce-unsat-cores was enabled.

Fixes cvc5/cvc5-projects#406.