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

Meanwhile, heat a large pot over medium-high heat. Add ground beef, bell peppers, and onion; cook and stir until browned and crumbly, 5 to 7 minutes. Drain and discard grease.

Add broth, crushed tomatoes, tomato soup, and mushroom pieces to the pot; bring to a boil. Reduce heat to medium-low, cover the pot, and simmer soup, stirring occasionally, until vegetables are tender, 30 to 40 minutes.

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