Researchers are looking for new ways to treat people with high-risk non-muscle invasive bladder cancer (HR NMIBC). NMIBC is cancer in the tissue that lines the inside of the bladder but has not spread to the bladder muscle or outside of the bladder. High-risk means NMIBC may have a high chance of getting worse or coming back after treatment. HR NMIBC can also include carcinoma in situ (CIS). CIS is bladder cancer that appears flat and is only in the inner layer (surface) of the bladder. CIS is not raised and is not growing toward the center of the bladder. The standard treatment for HR NMIBC is a procedure to remove the tumor called transurethral resection of the bladder tumor (TURBT) followed by Bacillus Calmette-Guerin (BCG). Standard treatment is something that is considered the first line of treatment for a condition. BCG is an immunotherapy, which is a treatment that helps the immune system fight cancer. However, BCG may not work to treat HR NMIBC in some people. Researchers want to learn if adding intismeran autogene, the study treatment, to standard treatment can help treat HR NMIBC. Intismeran autogene is designed to help a person's immune system attack their specific cancer. The goals of this study are to learn: * If people who receive intismeran autogene with BCG live longer without the cancer growing, spreading, or coming back, or dying from any cause, compared to people who receive BCG alone * If more people who receive intismeran autogene with BCG have their cancer go away (complete response), compared to people who receive BCG alone * How many people who receive intismeran autogene without BCG have their cancer go away