Test reports are generated after a Specification has finished execution and the generation is performed by the build system, so in your case by Gradle. Spock has no knowledge of that so you are unable to get that information from within the test.
You can on the other hand quite easily get that information from Gradle. Test task has two methods that might be of interest to you here: addTestListener() and afterSuite(). It seems that the cleaner solution here would be to use the first method, implement a test listener and put your logic in afterSuite() of the listener (and not the task configuration). You would probably need to put that listener implementation in buildSrc as it looks like you have a dependency on SauceREST and you would need to build and compile your listener class before being able to use it as an argument to addTestListener() in build.gradle of your project.