Perioperative Pembrolizumab (MK-3475) Plus Cystectomy or Perioperative Pembrolizumab Plus Enfortumab Vedotin Plus Cystectomy Versus Cystectomy Alone in Participants Who Are Cisplatin-ineligible or Decline Cisplatin With Muscle-invasive Bladder Cancer (MK-3475-905/KEYNOTE-905/EV-303)

Inclusion Criteria: * Have a histologically confirmed diagnosis of urothelial carcinoma/muscle-invasive bladder cancer \[MIBC\] (cT2-T4aN0M0 or T1-T4aN1M0) with predominant (≥50%) urothelial histology to be confirmed by Blinded Independent Central Review (BICR) (central pathology and/or imaging). * Clinically nonmetastatic bladder cancer determined by imaging * Eligible for radical cystectomy (RC) + pelvic lymph node dissection (PLND), and agreement to undergo curative intent standard RC + PLND (including prostatectomy if applicable) * Ineligible for treatment with cisplatin, as defined by meeting at least one of the following criteria OR be eligible for treatment with cisplatin but decline treatment with cisplatin-based chemotherapy: * Impaired renal function with measured or calculated creatinine clearance (CrCl) 30 to 59 mL/min (calculated by Cockcroft-Gault method, Modification of Diet of Renal Disease \[MDRD\] equations, or measured by 24-hour urine collection) * Eastern Cooperative Oncology Group (ECOG) Performance Status 2 * Common Terminology Criteria for Adverse Events (CTCAE) v.4 Grade ≥2 audiometric hearing loss * New York Heart Association (NYHA) Class III heart failure * Transurethral resection (TUR) of a bladder tumor that is submitted for central pathology assessment and adequate to determine urothelial histology and PD-L1 expression assessment * ECOG performance status of 0, 1, or 2 * Adequate organ function * A male participant is eligible to participate if he agrees to use contraception and refrain from donating sperm during the intervention period and for at least 180 days after the last dose of enfortumab vedotin. If the male participants are receiving pembrolizumab only or undergoing surgery only, there are no contraception requirements * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least 1 of the following conditions applies: Not a (woman of childbearing potential) WOCBP or a WOCBP who agrees to use a highly effective contraceptive method or be abstinent from heterosexual intercourse (as their preferred and usual lifestyle) during the intervention period and for at least 120 days after the last dose of pembrolizumab and at least 180 days after the last dose of enfortumab vedotin; whichever comes last. A female participant must agree not to donate eggs during this period as well * A WOCBP must have a negative highly sensitive pregnancy test within 24 hours before the first dose of study intervention Exclusion Criteria: * Known additional nonurothelial malignancy that is progressing or has required active anticancer treatment ≤3 years of study randomization, with certain exceptions * Has ≥ N2 or metastatic disease (M1) as identified by imaging * Received any prior systemic treatment, chemoradiation, and/or radiation therapy for muscle-invasive bladder cancer (MIBC) or non-muscle invasive bladder cancer (NMIBC) * Received prior therapy with an anti-programmed cell death protein 1 (PD-1), anti-programmed death-ligand 1 (PD-L1), or anti-programmed cell death 1 ligand 2 (PD-L2), or with an agent directed to another stimulatory or coinhibitory T-cell receptor * Received prior systemic anticancer therapy including investigational agents within 3 years prior to randomization * Received any prior radiotherapy to the bladder * Received a partial cystectomy of the bladder to remove any non-muscle-invasive bladder cancer (NMIBC) or MIBC * Received a live or live-attenuated vaccine within 30 days before the first dose of study intervention * Current participation in or participation in a study of an investigational agent or use of an investigational device within 4 weeks prior to the first dose of study intervention * Ongoing sensory or motor neuropathy Grade 2 or higher * Diagnosis of immunodeficiency or receipt of chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior the first dose of study drug. Physiologic replacement doses of corticosteroids are permitted for participants with adrenal insufficiency. * Hypersensitivity to monoclonal antibodies (including pembrolizumab) and/or any of their excipients * Severe hypersensitivity (≥ Grade 3) to enfortumab vedotin or any excipient contained in the drug formulation of enfortumab vedotin * Active keratitis or corneal ulcerations. Participants with superficial punctate keratitis are allowed if the disorder is being adequately treated in the opinion of the investigator * Active autoimmune disease that has required systemic therapy in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic therapy and is allowed * Has uncontrolled diabetes * History of (noninfectious) pneumonitis that required steroids, or current pneumonitis * Active infection requiring systemic therapy * Has had an allogeneic tissue/solid organ transplant