Preheat the oven to 250 degrees F. Cut the squash in half lengthwise, then halve each piece crosswise; remove the seeds. Transfer to a large glass bowl and add 1/4 cup water. Cover tightly with plastic wrap and microwave until just tender, 12 to 15 minutes. Uncover and let cool slightly.
Meanwhile, season the pork with salt and pepper. Heat a large nonstick skillet over medium-high heat, then add the olive oil. Working in two batches, add the pork and cook until browned and cooked through, about 2 minutes per side. Remove to a baking sheet and keep warm in the oven.
Melt the butter in the same skillet over medium heat. Add the capers and cook until sizzling, 1 minute. Add the wine and lemon juice. Increase the heat to high and bring to a boil. Add the broth; boil until reduced by half, 2 to 3 minutes. Keep warm over low heat.
Drain the squash and scrape the flesh into strands with a fork; discard the skin. Season with 1/4 teaspoon salt and a few grinds of pepper. Stir the herbs into the pan sauce and transfer to a liquid measuring cup. Return the skillet to medium heat and add the tomatoes. Cook, stirring occasionally, until slightly blistered, 2 to 3 minutes. Serve the pork with the squash and tomatoes; drizzle the squash and pork with the pan sauce.