Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the rice is tender and liquid has been absorbed, 20 to 25 minutes.

Heat a large pot over medium-high heat. Cook and stir beef, bell peppers, and onion in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.

Pour broth and tomato soup into the pot; add crushed tomatoes and mushroom pieces. Bring the soup to a boil, reduce heat to medium-low, cover the pot, and simmer the soup, stirring occasionally, until the vegetables are tender, 30 to 40 minutes.

Stir rice into the soup, breaking clumps into individual grains; cook until the rice is hot, about 5 minutes.