Make the lemon-garlic sauce: in a blender combine lemon zest and juice, minced garlic, and toasted walnuts; blend on high until smooth, about 30 seconds.
Add the grated Parmesan and 3 tablespoons of olive oil to the blender and blend until well combined; transfer the sauce to a small bowl and set aside.
Cook the spaghetti in a large pot of salted boiling water until al dente according to package directions; reserve 1 cup of the pasta cooking water, then drain the pasta.
Heat 1 tablespoon olive oil in a skillet over medium-high heat, add the baby capers and cook until crisp, about 3 minutes; transfer to a paper towel–lined plate to drain.
In the same skillet, add the remaining olive oil and reduce heat to medium; add the sourdough cubes and cook, stirring occasionally, until golden and crisp, 2–3 minutes; transfer to the plate with the capers.
Pat the salmon pieces dry and season with salt and black pepper. Melt the butter in the skillet over medium-high heat, add the salmon, and cook until just cooked through and fork-tender, 3–5 minutes; remove from the skillet and set aside.
Add the prepared sauce, drained spaghetti, and up to 1 cup reserved pasta water to the skillet; cook briefly over medium heat while tossing with tongs until the pasta is evenly coated and sauce is silky, adding more pasta water as needed.
Stir in the cooked salmon and watercress gently to combine and warm the watercress slightly without wilting it completely.
Serve the pasta topped with the crispy capers and toasted sourdough cubes and additional watercress if desired.
