Cut onion bulbs in half lengthwise (quarter if large). Cut enough onion tops into 2″ lengths to measure 1 cup. Heat 1 Tbsp. oil in a large skillet over medium-high heat until almost smoking. Add onion bulbs, cut side down; cook until golden, about 3 minutes. Transfer to a plate.

Heat 1 Tbsp. oil in same skillet. Add squash; cook, stirring occasionally, until golden brown and just tender, about 5 minutes. Stir in onion bulbs, 1 cup onion tops, and 1 Tbsp. thyme leaves; season with salt and pepper and cook until onion tops wilt, about 1 minute longer. Remove from heat; set squash mixture aside.

Heat remaining 2 Tbsp. oil in a large nonstick or cast-iron skillet over medium-high heat. Season halibut with salt. Add fish and thyme sprigs to skillet and cook until fish is golden brown, about 5 minutes. Turn fish and cook until just cooked through and opaque in the center, about 2 minutes longer. Divide onion-squash sauté among plates; top with halibut.