> inevitable difference between "true" and "provable" (ie Godel's incompleteness). Now that part is pretty much solved, we are fairly confident that the foundations of mathematics are consistent.

Your assertion about the inevitability is true only under specific axioms. If you are willing to drop the notion that infinity exists, or the law of excluded middle (and maybe others), the problems that arise from Gödel's incompleteness theorems don't necessarily apply.

I'm very far from mathematician circles so I don't know how they actually interpret Gödel, but the idea of being "fairly confident" that math foundations are consistent while knowing that either there are true statements that we can't prove, or that the foundations aren't consistent, feels like a pretty weird thing to me.

I always thought most mathematicians just looked at Gödel like he discovered an interesting novelty, then ignored him and went back to doing whatever math they were already doing, instead of losing sleep over what his theorem implied.