Add the sliced onions, butter, salt, and sugar to the slow cooker. Toss everything together so the onions are coated with butter.
Cover and cook on high for about 3 hours, stirring once or twice during cooking, until the onions soften and begin releasing their moisture.
Pour in the white wine and stir well. Continue cooking on high for another 1 to 2 hours, stirring occasionally, until the onions become deeply golden, soft, and slightly jammy.
For deeper color and better caramelization, leave the slow cooker lid slightly ajar for the final 30 minutes so excess moisture can evaporate.
If the onion strands are long, chop them lightly with a knife or kitchen scissors so they blend easily into the dip. Allow the onions to cool for a few minutes. Reserve 2 tablespoons of the caramelized onions for topping.
Reduce the slow cooker to warm or low heat. Add the softened cream cheese and stir until it melts and becomes smooth.
Stir in the sour cream, grated garlic, chives or parsley, and Worcestershire sauce. Mix until the dip is creamy and evenly combined.
Taste the dip and adjust the seasoning if needed. Transfer the dip to a serving bowl and serve slightly warm or chilled.
Transfer the dip to a serving bowl and serve slightly warm or chilled.