Heat olive oil in a large pot over medium heat. Cook whole chicken breast until browned, about 4 minutes per side. Transfer to a plate. Reduce heat to low; add onion, garlic, sazon seasoning, parsley, celery seeds, salt, and bay leaf. Cook and stir until onion is soft and fragrant, 5 to 8 minutes.
Stir grape tomatoes into the pot; cook until softened, about 2 minutes. Pour in chicken broth. Increase heat to high. Return chicken breast to the pot; add cannellini beans, chickpeas, brown rice, and peppercorns. Bring to a boil; cook for 5 minutes. Reduce heat to low, cover, and simmer until flavors combine, about 30 minutes.
Remove pot from heat; stir in spinach until wilted. Transfer chicken to a plate; shred using 2 forks. Stir shredded chicken back into the soup.