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.
Heat the extra-virgin olive oil in a small skillet over medium heat until shimmering. Add the sliced garlic and cook, stirring, until golden, about 3 minutes. Transfer garlic to paper towels with a slotted spoon to drain and crisp.
In a large skillet, heat 1 tablespoon of oil from the sun-dried tomato jar over medium-high heat. Add the chopped sun-dried tomatoes, washed spinach, and balsamic vinegar; cook, 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 to loosen the sauce; add more pasta water if needed for desired consistency.
Season with salt and black pepper to taste, toss to combine, then sprinkle with crumbled feta and the toasted garlic chips. Serve warm.