Season chicken breasts with salt and black pepper. Preheat the grill or grill pan to medium-high heat.
Grill chicken for about 6-8 minutes per side or until the internal temperature reaches 165°F (74°C).
Linguine: Fill a medium saucepan halfway with hot water, cover, and bring to a boil. Uncover; add 1 tsp salt and linguine, stirring occasionally. Cook until al dente, 8-10 minutes. Reserve ½ cup pasta water before draining.
Preheat a skillet over medium heat. Once hot, add olive oil, garlic, and onion. Cook until softened, 3-4 minutes.
Add tomatoes, salt, and pepper to the skillet. Cook until tomatoes begin to soften, 3-4 minutes.
Add spinach in handfuls, allowing it to wilt slightly between additions. Crumble goat cheese into the skillet, add cream, and stir until melted and combined, 3-4 minutes.
Add drained pasta to the skillet and toss to combine. Add reserved pasta water if needed for desired consistency.
Arugula Salad: Combine shallot, olive oil, red wine vinegar, honey, mustard, salt, and pepper in a jar. Shake to emulsify.
In a large bowl, toss arugula with enough vinaigrette to coat the leaves.
Season with additional salt and pepper. Top with toasted pine nuts and shaved parmesan.
In a pitcher, combine the ingredients for the lemon sparkling water.
Serve: Serve the grilled chicken over linguine, alongside arugula salad. Pour lemon sparkling water into glasses with ice cubes if desired.