What is the best substitute for eggs when baking cookies?

I do a lot of vegan baking and I was wondering what the best substitute is for eggs in cookies? Lately I have been using aquafaba and extra baking soda, but maybe using that is just as effective as using water?

I don't know much about the science of baking, but I would really like to learn it as I find it very interesting. Maybe if I know more about it I will find substitutions easier.

I've read many places that applesauce and carbonated water are good substitutes too; is that true?

If I were to replace the eggs in the following recipe, what substitution would be best?

Ingredients 3 cups (380 grams) all-purpose flour 1 teaspoon baking soda 1 teaspoon fine sea salt 2 sticks (227 grams) unsalted butter, at room temperature 1/2 cup (100 grams) granulated sugar 1 1/4 cups (247 grams) lightly packed light brown sugar 2 teaspoons vanilla 2 large eggs, at room temperature 2 cups (340 grams) semi sweet chocolate chips

Directions Preheat oven to 350ºF. Line baking sheets with parchment paper. In a medium bowl combine the flour, baking soda, and salt. In the bowl of an electric mixer beat the butter, granulated sugar, and brown sugar until creamy, about 2 minutes. Add the vanilla and eggs. Gradually beat in the flour mixture. Stir in the chocolate chips. If time permits, wrap dough in plastic wrap and refrigerate for at least 24 hours but no more than 72 hours. This allows the dough to “marinate” and makes the cookies thicker, chewier, and more flavorful. Let dough sit at room temperature just until it is soft enough to scoop. Divide the dough into 3-tablespoon sized balls using a large cookie scoop and drop onto prepared baking sheets. Bake for 12-15 minutes, or until golden brown. Cool for 5 minutes before removing to wire racks to cool completely.