Causal inference offers a principled framework for understanding how interventions influence software behavior, yet its adoption in software testing remains fragmented across different tasks and research communities. In this rapid review, we systematically analyze 27 studies that apply causal reasoning to software testing activities such as debugging, fairness assessment, and performance evaluation. We organize the literature using a layered causal inference pipeline, spanning causal representation, structure discovery, identification, and effect estimation, to reveal how existing work maps onto fundamental causal reasoning stages. Our analysis shows a concentration of research on identification and estimation, while representation and discovery techniques are underexplored in testing contexts. We also identify cross-layer challenges, including model misspecification, untested assumptions, and limited empirical evaluation, which hinder practical application. Based on these insights, we propose a research agenda that highlights underrepresented opportunities for advancing causal methods in software testing. This structured perspective aims to unify disparate contributions and guide future empirical and methodological work in the intersection of causality and software testing.