I tried to build a statically linked binary. The build works fine but it's not possible to execute the binary. I did a simple test by adding this line to your existing workflow. It fails with

thread 'main' panicked at 'already borrowed: BorrowMutError', /home/runner/.cargo/registry/src/github.com-1ecc6299db9ec823/pyo3-0.17.3/src/gil.rs:433:52

You can see the full build here: https://github.com/kkrampa/PyOxidizer/actions/runs/3925221913/jobs/6710342865