I'm not sure I understand your argument. Z3's API is canonically C. There's a C++ wrapper that works pretty well. I don't have experience with the Rust wrapper, but I'd imagine that works pretty well too.
"first-class support for returning errors and propagating them" certainly sounds like exceptions! In fact, the compiler can even emit special tables that let the runtime completely skip over stack frames that don't need to do any cleanup during that propagation step!
Some languages have even innovated new kinds of exceptions that you can throw but that you are admonished should almost certainly never be caught.
Unfortunately even this is also better for tool support, a problem that using a bunch of macros solves. It's cool and good when a variable gets declared inside the guts of some macro expansion (and--critically--escapes those guts).