@SaveByRichter35 your lawn looks FANTASTIC!! Most people would have been happy with the before pictures, but the dethatching after shot shows the true story. Just because a lawn may be green, doesn't mean it is healthy.
chile57, like SaveByRichter says, definitely add soil into your levelling to take out the humps and bumps. Also, once you do level it, make sure you use a roller to compact it depending on how deep the valleys are. And to also echo what SBR says, remove the clay plugs after aerating, no point in re-introducing that material. That can be a pain in the ass and very tedious to do, but worth the effort.