Thank you all very much for your responses. I'll try to sum up some answers to questions and explanation below...
Flipflopgirl, I completely agree about modern cast iron being finicky and it's good to know someone else is googling the issue. I prefer my old Griswold
In this instance, I'm referring to my enameled Staub cast iron, and I don't believe it should really take a "seasoning", though Staub claims (as opposed to Le Creuset) that their pans get better after use. I will however contact Staub to see what they have to say regarding the stickiness.
Cheflayne, I did indeed follow what I understand to be Staub's break-in/"seasoning" procedure - heating oil to its smoking point then washing the pot. However, I did not do this before I first experienced the fibers clinging to the pan. From my understanding, I agree that you can't season enamel like you can cast iron, but it is interesting to me that some folks seem to believe that Staub can get better with some application of remnant oils/fats.
Millionsofknives, I don't care too much about drying. The issue arose because I cooked food, then I washed it, then after drying the pan had irridescent stains and water spots, so I wiped on some avocado oil as I do my cast iron between uses, and when I did this paper towel fibers got stuck all over the inside of the pot. From there I began to figure out how to dry the pan over heat and minimally contact it to apply some oil. I am now considering not using that oiling step.
MaryB, I understand and agree with you. My issue originated with the irridescent staining and water spots. I don't have any issues with sticking as I have used proper methods when cooking in it.
ChicagoTerry, I am planning on following this basic procedure that you mention. Only problem is that when I wipe it dry after washing, fibers are all over it! So then the question is do I wash it out with water right then to remove fibers and dust, or do that right before I cook the next meal.
Honestly, this is a silly situation to be debating, I understand, but I can't get the pot clean without fibers and dust unless I air dry/heat dry and leave stains. I suppose stains are preferrable. I just want to get cooking!