Using the saute setting on the Instant Pot or your air fryer lid, cook the bacon until crispy. Remove the bacon to dry between paper towels, keeping the bacon drippings in the inner pot. When the bacon has cooled, break it into small pieces.
Set the Instant Pot to saute on high for 5 minutes, leaving the bacon drippings in the pot. Cook the potatoes, carrots, celery, onions, and garlic in the drippings.
Pour in the clam juice and deglaze. Add the tomato juice, diced tomatoes and juices, tomato paste, and liquid from the canned clams (but not the clams), salt, pepper, crushed red pepper, and bay leaves. Tie the fresh parsley and thyme sprigs together with cooking twine and put into the pot. Close and seal the pressure cooker lid. Set to pressure cook (manual) on high for 10 minutes.
When complete, do a controlled quick release of the pressure. Open the lid and remove/discard the bay leaves and sprigs of parsley and thyme. Stir in the reserved canned clams. Taste and season with additional salt and pepper if desired.
Serve warm topped with the cooked bacon bits, extra crushed red pepper flakes and fresh parsley or thyme.