Heat a large straight-sided skillet over medium-high heat; swirl in oil. Add onion, season with salt, and cook, stirring occasionally, until just softened, about 2 minutes. Add tomatoes and juices and simmer, stirring occasionally, until thickened and reduced slightly, about 5 minutes.
Stir in rice and 2 1/2 cups water, then return to a simmer. Cover, reduce heat to low, and cook until rice is tender, about 12 minutes. Stir in shrimp and spinach and simmer, covered, until shrimp is just pink and opaque, about 4 minutes. Season with salt and pepper. Serve, sprinkled with feta and mint and drizzled with oil.