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Cut each tomato into quarters and cut each quarter in half again; transfer to a medium bowl. Add extra-virgin olive oil and vinegar; season with salt and pepper. Toss to combine and set salsa aside.
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Melt unsalted butter in a medium skillet over medium-high heat. Add mushrooms and season with sugar, salt, and pepper. Cook, stirring occasionally, until slightly softened, 3 to 4 minutes. Remove from heat and stir in thyme and rosemary. Set aside and keep warm.
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Heat olive oil in a large skillet over medium-high heat. Add spinach and cook, stirring constantly, until spinach is wilted, about 1 minute. Season with salt and pepper; remove from heat, set aside, and keep warm.
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Score each side of scallops in a crosshatch pattern; season with salt and pepper, rubbing into scored surface. Heat 1 tablespoon salted butter in a medium nonstick pan. Add scallops and cook, without stirring, 3 to 4 minutes. Add remaining tablespoon salted butter to skillet and turn scallops. Cook without stirring, 3 to 4 minutes. Remove scallops from heat and squeeze lemon over scallops.
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To serve, divide spinach evenly between 4 plates; top each with a scallop. Garnish with tomato salsa and mushrooms.