Preheat oven to 190°C (375°F). Arrange the whole-wheat sourdough on a baking sheet, drizzle with 1 tbsp olive oil, coat both sides, and bake 8–10 minutes, flipping once, until golden and crisp. Rub one side of each slice with the cut side of the halved garlic clove; set aside.
Heat the remaining 2 tbsp olive oil in a large, deep skillet or braiser over medium heat. Add shallots and fennel; cook 5–7 minutes until softened and translucent, not browned. Stir in minced garlic and red pepper flakes; cook 1 minute until fragrant.
Add cherry tomatoes and sun-dried tomatoes. Increase heat to medium-high; cook 4–5 minutes, stirring occasionally, until tomatoes begin to collapse. Pour in white wine; bring to a vigorous simmer and reduce 4–5 minutes, to about half.
Stir in 1 cup drained cannellini beans, the low-sodium vegetable broth, and bay leaf. Return to a boil, then reduce to a steady simmer. Cook uncovered 15 minutes to meld flavors and slightly thicken.
Pat sea bass dry. Season flesh sides with 1/8 tsp of the sea salt and black pepper. Nestle fillets into the simmering sauce, skin-side down. Cover and poach 5–7 minutes, until opaque and flaking easily or the thickest part reaches 60°C (140°F).
Carefully transfer fish to a warm plate; discard bay leaf. Stir parsley and torn basil into the sauce. Squeeze in lemon juice to taste and season with the remaining 1/8 tsp sea salt if needed.
To serve, place two garlic crostini in each shallow bowl. Spoon the tomato-bean sauce over the bread, set a fish fillet on top, and ladle more sauce around. Serve immediately with a lemon wedge.