TLA+ has also had an SMT-based backend, Apalache [1], for a few years now. In general, you encode your system model (which would be the Rust functions for Verus, the TLA model for Apalache) and your desired properties into an SMT formula, and you let the solver have a go at it. The deal is that the SMT language is quite expressive, which makes such encodings... not easy, but not impossible. And after you're done with it, you can leverage all the existing solvers that people have built.
While there is a series of "standard" techniques for encoding particular program languages features into SMT (e.g., handling higher-order functions, which SMT solves don't handle natively), the details of how you encode the model/properties are extremely specific to each formalism, and you need to be very careful to ensure that the encoding is sound. You'd need to go and read the relevant papers to see how this is done.
While there is a series of "standard" techniques for encoding particular program languages features into SMT (e.g., handling higher-order functions, which SMT solves don't handle natively), the details of how you encode the model/properties are extremely specific to each formalism, and you need to be very careful to ensure that the encoding is sound. You'd need to go and read the relevant papers to see how this is done.
[1]: https://apalache.informal.systems