Begin by scrubbing the red potatoes under cold running water, then cut them into evenly-sized chunks. Place the potatoes in a large pot and cover them with water, adding a pinch of salt. Bring the pot to a boil over high heat, then reduce the heat to a simmer. Cook for about 10-15 minutes, or until the potatoes are fork-tender yet firm.

While the potatoes are cooking, heat a skillet over medium heat. Add the slices of thick-cut bacon, cooking for 10-15 minutes or until crispy and browned. Transfer to a plate lined with paper towels to drain excess grease. Allow the bacon to cool before chopping it into bite-sized pieces.

In a large mixing bowl, combine the chopped bacon, mayonnaise, Caesar dressing, grated Parmesan cheese, white vinegar, and Worcestershire sauce. Add celery salt, diced celery, and minced red onions. Stir well until all ingredients are thoroughly blended, creating a creamy dressing for the Caesar Potato Salad.

Once the potatoes have cooled slightly, drain them and add them to the bowl with the dressing mixture. If using hard-boiled eggs, chop them coarsely and add them in. Gently toss everything together until the warm potatoes are well-coated in the creamy mixture.

Cover the bowl with plastic wrap and place it in the refrigerator. Allow the salad to chill for at least 4 hours, or preferably overnight, to develop its rich flavors.