This appears to be failing with

OSError: cannot load library '/__w/arrow-rs/arrow-rs/go/arrow/internal/cdata_integration/arrow_go_integration.so': /__w/arrow-rs/arrow-rs/go/arrow/internal/cdata_integration/arrow_go_integration.so: cannot open shared object file: No such file or directory. Additionally, ctypes.util.find_library() did not manage to locate a library called '/__w/arrow-rs/arrow-rs/go/arrow/internal/cdata_integration/arrow_go_integration.so'

@pitrou perhaps you might be able to advise here?

You need to enable the Go integration build like here:
https://github.com/apache/arrow/blob/5978729277e164c5b4dfd8916bb410b9e67a04c7/docker-compose.yml#L1735

      ARROW_GO_INTEGRATION: 1

Note this will enable the C Data Interface tests only for the supported implementations (C++ and Go currently).

To actually test the C Data Interface in Rust you'll need a bit more work.
See for example how C++ works here:
https://github.com/apache/arrow/blob/5978729277e164c5b4dfd8916bb410b9e67a04c7/dev/archery/archery/integration/tester_cpp.py#L146-L245

I've created #4867 as a follow up to enable the new tests