Well, by "understanding" I mean "understanding by humans", indeed.

That’s a strange delineation. Engineering is essentially about designing a thing, asking whether that thing really does satisfy the desired criteria, and then iterating when it does not. Mathematical models of the world are tremendously useful to this practice—engineers don’t need to guess about many aspect of the real world: they have physics. What they want, more than anything else, is strong evidence that a property holds. Internal validity (proof) and external validity (experiment) are the best evidence that you can get—why would you throw one of those approaches away?

I would call it "Engineered (as machine-made trustworthy) Mathematics": you have results but nobody undrstands them but they were not produced by humans.

Despite that, people use them. In that sense, similar to the Finite Elements method. But the tools (statements) are machined like any other tool (screwdriver).

Similar to microprocessors in your example. But about statements.

You might have gotten it backwards. Proofs are essentially rooted trees

The details could be painful but having a birds eye view is always possible?

And having a machine compress it for human consumption, sounds very plausible (and which I think of as engineering)