Mix together garlic powder, onion powder, paprika, salt, and pepper in a bowl. Sprinkle on both sides of chicken tenders.
Heat olive oil in a large skillet over medium heat. Add chicken tenders and sear until browned, about 3 minutes per side. Remove to a plate and loosely tent with foil.
Reduce heat to medium and melt butter in the skillet. Add mushrooms and onion and cook until mushrooms start to brown, about 4 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
Whisk together half-and-half, chicken broth, lemon juice, 2 tablespoons dill, and cornstarch in a medium bowl; add to the skillet. Stir until sauce is slightly thickened, about 3 minutes, and season with salt and pepper.
Reduce heat to low, add chicken and any accumulated juices to the pan. Simmer until chicken is no longer pink in the center and the juices run clear, 4 to 5 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Sprinkle the remaining tablespoon of dill on top of chicken, and serve with lemon wedges.