DESTINY-Endometrial01: An Open-Label, Sponsor-Blinded, Randomized, Controlled, Multicenter, Phase III Study of Trastuzumab Deruxtecan (T-DXd) Plus Rilvegostomig or Pembrolizumab vs Chemotherapy Plus Pembrolizumab as First-Line Therapy of HER2-Expressing (IHC 3+/2+), Mismatch Repair Proficient (pMMR), Primary Advanced or Recurrent Endometrial Cancer

* Key Inclusion Criteria: * Participants must be ≥ 18 years of age at the time of screening. Other age restrictions may apply as per local regulations. * Histologically confirmed diagnosis of epithelial endometrial carcinoma. All histologies are allowed except for sarcomas (carcinosarcomas are allowed). * Following surgery or diagnostic biopsy, participant must have primary advanced disease (Stage III/IV) or first recurrent endometrial cancer and meet at least one of the following criteria: * Primary Stage III (per FIGO 2023) disease with measurable disease at baseline per RECIST 1.1 based on the investigator's assessment. * Primary Stage IV disease (per FIGO 2023) regardless of presence of measurable disease at baseline. * First recurrent disease regardless of presence of measurable disease at baseline. * Endometrial cancer with HER2 IHC expression of 3+ or 2+ as assessed by prospective central testing. * Endometrial cancer that is determined pMMR by prospective central IHC testing. * Provision of adequate FFPE tumor tissue sample of a tumor lesion that was not previously irradiated for central HER2, MMR, and PD-L1 IHC testing and valid central test results for randomization/ stratification. * Prior therapy: * Naïve to first-line systemic anticancer therapy. Participants may have received one prior line of adjuvant/neoadjuvant chemotherapy with curative intent (chemotherapy or chemoradiation) if disease recurrence or progression occurred ≥ 6 months after last dose of chemotherapy. Prior trastuzumab in the adjuvant/neoadjuvant setting is allowed. * No prior exposure to ADCs or immune checkpoint inhibitors including (but not limited to) anti-PD-1/PD-L1/PD-L2 and anti-CTLA-4 antibodies and therapeutic anticancer vaccines. * Participants may have received prior radiation therapy for the treatment of endometrial cancer. Prior radiation therapy may have included pelvic radiation therapy, extended field pelvic/para-aortic radiation therapy, and/or intravaginal brachytherapy. Adequate treatment washout period is required. * Eastern Cooperative Oncology Group performance status (ECOG PS) 0-1. * Left ventricular ejection fraction (LVEF) ≥ 50% within 28 days before randomization. * Adequate organ and bone marrow function within 14 days before randomization. * Key Exclusion Criteria: * History of organ transplant * Uncontrolled intercurrent illness, including, but not limited to ongoing or active known infection, serious chronic gastrointestinal conditions associated with diarrhea and active non-infectious skin disease requiring systemic treatment. * Spinal cord compression or clinically active central nervous system metastases * Participants with a medical history of myocardial infarction (MI) within 6 months before randomization, or symptomatic congestive heart failure (CHF) (NYHA Class II to IV), clinically significant arrhythmia, or cardiomyopathy of any etiology. Participants with troponin levels above ULN at screening (as defined by the manufacturer), should have a cardiologic consultation before enrollment to rule out MI * History of (non-infectious) ILD/pneumonitis that required steroids, current ILD/pneumonitis, or suspected ILD/pneumonitis that cannot be ruled out by imaging at screening. * Lung criteria: * Lung-specific intercurrent clinically significant illnesses including, but not limited to, any underlying pulmonary disorder (e.g., pulmonary emboli within 3 months of the study enrollment, severe asthma, severe chronic obstructive pulmonary disease (COPD), restrictive lung disease, pleural effusion etc.). * Any autoimmune, connective tissue or inflammatory disorders where there is documented, or a suspicion of pulmonary involvement at the time of screening. * Prior pneumonectomy (complete). * Active or prior documented autoimmune or inflammatory disorders requiring chronic treatment with steroids or other immunosuppressive treatment. * Active primary immunodeficiency/ active infectious disease(s) including: * Tuberculosis (TB) * HIV infection that is not well controlled. * Chronic or active hepatitis B, chronic or active hepatitis C; however, participants who have chronic hepatitis B and are receiving suppressive antiviral therapy are allowed to be enrolled if alanine aminotransferase (ALT) is normal and viral load is controlled. * Any concurrent anticancer treatment without an adequate washout period prior to the first dose of study intervention. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., HRT) is allowed.