Right, coherentism and correspondence map nicely with empirical and logical truths, except that one can discover logical truths empirically (but not empirical truths by just thinking about it).

That’s why people talk of “experimental” mathematics, done by computer searches for patterns. But it’s not experimental, or empirical, in the same sense in which science is.

As for your last question, I think the concept of truth is a human one, and hence mind-dependent. Of course, facts about the world are what they are regardless of the existence of minds, but the term truth is applicable to sentences about the world, not the world itself.

Now, are there mind-independent facts about mathematics or logic? That depends on whether one is a Platonist about math or logic. I’m not: Smolin on mathematics