In a medium skillet over medium-high heat, warm the oil until it shimmers. Add the capers and green onions and cook, stirring occasionally, until the onions start to soften, no more than 1 minute. Pour the contents of the pan into a small heatproof bowl and let sit for a few minutes. Stir in the soy sauce, vinegar, lemon juice, and honey. Set the vinaigrette aside.
Cut the salmon into ½-inch slices, trimming away any gray or brown bits. Cut the avocado in half lengthwise, remove the pit, and dice the flesh. Squeeze the lemon wedge over the pieces to prevent browning.
Bring a large pot of salted water to a boil over high heat and have a large bowl of ice water ready. Add the spaghetti to the pot and cook according to the package instructions until slightly past al dente. Drain the spaghetti and plunge it into the ice water, using your hands to mix the strands and ensure they get evenly chilled. Drain again and press to squeeze out any excess water.
Put the spaghetti in a serving bowl and stir in the vinaigrette to evenly coat. Gently mix in the avocado and lay the salmon on top. Sprinkle herb sprigs over the top and serve.