Testing the Addition of an Anti-Cancer Immunotherapy Drug, Avelumab, to Gemcitabine and Carboplatin Chemotherapy Prior to Surgery in Muscle Invasive Urinary Tract Cancer vs. Surgery Alone in Patients Who Are Not Able to Receive Cisplatin Therapy (SWOG GAP TRIAL)

Inclusion Criteria: * Participants must have one of the following: * Histologically documented muscle-invasive bladder carcinoma (MIBC) from transurethral resection of bladder tumor (TURBT) within 56 days prior to registration * Histologically confirmed high grade upper tract urothelial carcinoma (UTUC) within 56 days prior to registration, with invasion confirmed by either a mass on cross-sectional imaging or a tumor directly visualized during upper urinary tract endoscopy within 56 days prior to registration * Participants diagnosed with mixed urothelial carcinoma and variant histology within 56 days prior to registration may be eligible if the majority (\> 50%) of the tumor consists of urothelial carcinoma. Participants with pure non-urothelial variant histologies or any small cell histology are not eligible * Participants must have clinical stage T2-T4aN0M0 bladder or upper tract cancer confirmed by radiologic staging (computed tomography \[CT\] scan/magnetic resonance imaging \[MRI\] abdomen and pelvis, and CT scan/x-ray of the chest) within 56 days prior to registration * Participants must have a bone scan within 56 days prior to registration if they have bone pain or elevated serum alkaline phosphatase * Participants must have a bimanual examination under anesthesia within 56 days prior to registration * Participants must not have received prior systemic chemotherapy, immunotherapy or radiotherapy for the treatment of muscle invasive bladder cancer (MIBC) or up…