Heat a large pot over medium-low heat until hot. Add the bacon and let it sizzle until the fat is rendered and the meaty bits are crunchy, 18 to 20 minutes. Transfer to paper towels to drain.
Generously season the rabbit with salt and pepper. Raise the heat to medium high and sear the rabbit in the fat, working in batches if needed, until golden brown, 6 to 8 minutes per side. Transfer to a plate and set aside.
If the pot is dry add a drizzle of olive oil. Lower the heat to medium, add the mushrooms, onions, and bay leaves and cook, stirring occasionally, until deeply colored, 18 to 22 minutes. Add the garlic and cook for 1 minutes more.
Pour in the wine and let it burble for 30 seconds, then nestle in the rabbit pieces. Squash the tomatoes with your hands over the pot and add them along with their juice, the 2 parsley sprigs, oregano, and sage.
Bring the mixture to a boil, reduce the heat to low, add the reserved liver, and simmer, covered, until the rabbit is cooked through, about 1 hour. Toss the parsley and bay leaves. Taste the liquid and season with salt and pepper, if needed.
If you're so inclined, transfer the rabbit to a platter and with a slotted spoon scoop the vegetables into a small bowl. Turn the heat under the pot to high to thicken the liquid. Otherwise, arrange the rabbit in the middle of the platter and spoon the mushrooms, onions, and tomatoes on top. Sprinkle with the bacon. Pour a bit of the liquid over the top and serve the rest on the side. Shower the dish with parsley just before serving.