Combine the red wine vinegar, 2 tablespoons water, sugar, and salt in a small bowl. Stir until the sugar dissolves.
Add the sliced red onion and toss to coat. Let the onions sit at room temperature for 30 minutes, or refrigerate them up to 3 days.
Bring a pot of water to a gentle simmer. Add the white vinegar.
Crack each egg into a small cup, then gently slide them into the simmering water. Poach for 3-4 minutes until the whites are set but the yolk remains runny. Remove with a slotted spoon.
While the eggs poach, toast the sourdough slices until golden. Butter each slice immediately.
Cut the avocados in half, scoop the flesh into a bowl, and mash it with a fork. Fold in the garlic, red pepper flakes, lemon juice, sea salt, and black pepper until combined but still chunky.
Divide the avocado mixture evenly between the toast slices.
Top each toast with 2 ounces of smoked salmon, arranged in folds. Carefully place one poached egg on top of each toast.
Drain the pickled red onions and scatter them over eggs. Top with the capers, everything bagel seasoning, red pepper flakes, and fresh dill. Finish with fleur de sel.