Place eggs in a single layer in a medium saucepan and cover with cold water by about an inch (2.5 cm). Bring to a rolling boil over medium-high heat. Remove from heat, cover, and let sit for exactly 12 minutes.
Transfer eggs to an ice water bath with a slotted spoon and cool for at least 5 minutes. Peel under cool running water, pat dry, and chop into rough 1/2-inch (1.25 cm) pieces.
Open both cans of tuna and pour into a fine mesh strainer. Press down firmly with a spoon or fingers to squeeze out as much liquid as possible. Transfer to a large mixing bowl and flake with a fork.
Rinse celery and dice into small 1/4-inch (6 mm) pieces. Peel and mince red onion as finely as possible. Soak minced onion in cold water for 5 minutes to reduce sharpness if desired, then drain and pat dry.
In the bowl with the tuna, combine mayonnaise, mustard, sweet pickle relish, and lemon juice. Stir until smooth and well-blended. Taste the dressing and adjust with more lemon juice or mustard if desired.
Add the flaked tuna, diced celery, and minced red onion to the dressing. Fold together gently with a rubber spatula or large spoon until everything is evenly coated. Fold in chopped hard-boiled eggs last, using a light hand to keep egg chunks intact.
Add optional fresh dill, chives, garlic powder, or paprika if using. Season generously with salt and fresh cracked black pepper, tasting as you go. Canned tuna already contains sodium, so taste before salting.
Cover and refrigerate for at least 20 to 30 minutes before serving to allow flavors to meld. When ready to serve, give it a quick stir and adjust seasoning with salt, pepper, or lemon juice as needed.