**Study Overview:** This study aims to test the safety and effectiveness of a new drug combination involving T-DXd (trastuzumab deruxtecan) and rilvegostomig, or T-DXd alone, compared to standard chemotherapy treatments (gemcitabine, cisplatin, and durvalumab) for people with advanced biliary tract cancer (BTC) that shows HER2 protein. HER2 is a protein that can affect the growth of cancer cells. The study includes adults aged 18 and older who have not received previous treatment for their advanced BTC. Participants need to provide a tumor sample and have specific health conditions checked, like heart and bone marrow function. **Key Points:** - **Duration & Visits:** Participants will need to regularly visit the study site for treatment and check-ups. - **Treatment:** This study involves receiving new drugs to compare with standard chemotherapy. - **Risks:** There might be side effects, and not everyone is eligible, such as those with certain heart issues or infections. Before joining, discuss with your doctor to understand if this study is suitable for you and what to expect during participation.