Your Jenkins pipeline could just be a singe step:

    run 'sh ./build.sh && ./test.sh && ./deploy.sh'

We have gone for middle ground, the pipeline has a small number of discrete steps, but these steps mainly just call scripts defined besides the code within the respective repo. That way one can replay the process manually wherever needed, but we still can easily see in Jenkins where the process fails, including submitting test results to jenkins to see directly in the web-ui which tests failed.