Heat oven to 425°F. Line a large rimmed sheet pan with parchment.
Whisk olive oil, garlic, lemon juice, zest, oregano, thyme, paprika, salt, pepper, and red pepper flakes.
Toss tomatoes, red onion, artichokes, olives, and capers with half the marinade on the pan. Spread in an even layer.
Pat salmon dry. Nestle pieces skin-side down on the vegetables. Spoon remaining marinade over the salmon.
Bake 12–15 minutes, until salmon flakes easily and reaches 125–130°F in the thickest part.
Broil 1–2 minutes for light browning, if desired. Remove and rest 3 minutes.
Scatter feta and parsley over the pan. Serve warm with pan juices.