Roughly chop the shrimp. Set aside about one-quarter of the shrimp in small chunks.
Place the remaining shrimp in a food processor with the garlic, smoked paprika, salt, and pepper. Blend until mostly smooth. Add the reserved chopped shrimp and pulse briefly so small pieces remain.
Transfer the shrimp mixture to a bowl. Stir in scallions, panko, and the beaten egg until a thick mixture forms. Shape into burger patties.
Place patties on a tray, cover, and refrigerate for 30 minutes to help them firm up.
Prepare the salsa by grilling or pan-roasting the pineapple and red onion for 2–3 minutes per side until lightly charred. Add all salsa ingredients to a food processor and blend until slightly chunky. Chill until ready to use.
Heat a cast iron skillet or griddle over medium-high heat (about 425°F). Add 1–2 tablespoons oil.
Cook shrimp burgers for 4–5 minutes per side until golden, crispy on the outside, and cooked through.
Serve shrimp patties on toasted buns topped with pineapple habanero salsa.