Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 18 to 20 minutes. Remove from heat and pour enough cold water on top of the cooked rice to cover it. Stir to cool. Drain well; transfer rice into a bowl. Stir in 1 tablespoon olive oil and season with herb salt.
Mix capers, parsley, and lemon zest in a small bowl; add to rice. Mix in zucchini, carrots, yellow bell pepper, and red bell pepper. Season with remaining 1 tablespoon olive oil, lemon juice, and salt.