The purpose of this Phase III study is to evaluate the efficacy and safety of sonesitatug vedotin in combination with capecitabine with or without rilvegostomig in 1L CLDN18.2-positive, HER2-negative gastric, GEJ, and esophageal adenocarcinoma, and the clinical performance of the investigation in vitro diagnostics (IVDs). The study will include 2 cohorts to provide a treatment option for all participants that are HER2-negative and CLDN18.2-positive. Cohort 1 will evaluate sonesitatug vedotin in combination with rilvegostomig with capecitabine in participants who are CLDN18.2-positive and programmed death-ligand 1 (PD-L1) positive. Cohort 2 will evaluate sonesitatug vedotin in combination with capecitabine in participants who are CLDN18.2-positive and PD-L1 negative or immune checkpoint inhibitor (ICI) ineligible.