Combine squash and thyme in a medium bowl. Crush 1 garlic clove; add to squash mixture.
Drizzle with 1 tablespoon oil; sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Toss to coat. Arrange squash mixture in a single layer on a baking sheet; bake at 375 for 40 minutes or until squash is tender; stirring occasionally.
Prepare grill.
Place 1 garlic clove in a mini food processor; process until finely chopped.
Add 2 tablespoons oil, celery leaves, parsley, juice, and 1/8 teaspoon salt; process until finely chopped.
Sprinkle 1/4 teaspoon salt and remaining 1/4 teaspoon pepper evenly over trout fillets.
Brush fillets with 1 teaspoon oil.
Place fillets, skin side down, on a grill rack; grill 5 minutes or until fish flakes easily when tested with a fork. Keep warm.
Slice remaining clove of garlic.
Heat a large skillet over high heat; add remaining 2 teaspoons oil.
Add sliced garlic, onion, and remaining 1/8 teaspoon salt; cook 2 minutes or until onions begin to brown.
Add squash mixture; cook 2 minutes or until hot. Stir in pecans; cook 1 minute. Divide squash mixture evenly among 4 plates; top each with a trout fillet. Spoon 2 tablespoons pesto over each trout fillet.