In a large pot of rapidly boiling salted water, cook soba noodles until al dente according to package instructions; drain.
Meanwhile, in a large bowl, whisk together tamarind, sugar, 2 tablespoons oil, lime juice, and cayenne. Add drained noodles, cilantro, onion, half the papaya, and all but 3 tablespoons of the peanuts; season with salt and pepper and toss to combine.
In a large skillet, heat the remaining 2 tablespoons oil over low. Add garlic and cook until golden brown on both sides, about 5 minutes total. Remove garlic chips and set aside on a paper towel. Raise heat to medium-high; add shrimp, sprinkle with coriander, salt, and pepper, and cook, tossing occasionally, until shrimp are just cooked through, about 3 minutes.
To serve, divide noodles and shrimp evenly among four large bowls; top each serving with remaining papaya, peanuts, garlic chips, and cilantro.