Bring a large pot of water to a boil; stir in 1 tbsp kosher salt.
Add potatoes; simmer until just tender, 10–12 minutes.
Drain well; spread on a sheet pan to steam-dry for 5 minutes.
Whisk mayonnaise, mustard, vinegar, Cajun seasoning, hot sauce, garlic powder, 3/4 tsp salt, and pepper.
Fold warm potatoes into the dressing until evenly coated.
Stir in celery, bell pepper, red onion, pickles, and most green onions.
Gently fold in chopped hard-boiled eggs.
Cover and chill at least 30 minutes to let flavors meld.
Top with paprika and remaining green onions; adjust seasoning to taste.
Serve cold or slightly cool.