Bring a large pot of salted water to a boil and cook the spaghetti until al dente, about 7 minutes; reserve 1 cup of the pasta cooking water, then drain the pasta.
In a small skillet over medium heat, warm 1/4 cup extra-virgin olive oil until shimmering. Add the sliced garlic and cook, stirring, until golden, about 2–3 minutes. Transfer the garlic to paper towels with a slotted spoon to drain and crisp.
In a large skillet, heat 1 tablespoon of the oil from the jar of sun-dried tomatoes over medium-high heat. Add the chopped sun-dried tomatoes and the washed spinach, then add the balsamic vinegar.
Sauté the tomatoes and spinach, stirring, until the spinach is wilted, about 3–4 minutes.
Add the drained spaghetti to the skillet with the tomatoes and spinach. Stir in 1/2 cup of the reserved pasta water (add more as needed to loosen the sauce) and toss to combine.
Season to taste with salt and black pepper, then sprinkle the pasta with crumbled feta and the toasted garlic chips. Serve warm.