Examples I haven't seen mentioned yet: Firefox. Atom/VSCode (Sublime Text clones). Android (iOS clone). Various databases (postgres, mongodb, etc). Reddit (Digg alternative, since closed source) though I'm not sure releasing their source code had anything to do with their success. HashiCorp in general sort of counts though it's harder to say "it was competing against X".
Care to elaborate in what ways Firefox counts as successful? Maybe it had a brief period of success ( maybe ) but that was long ago.
There are many ways to measure success, perhaps the easiest (though not necessarily the best) is money. Mozilla currently has net assets of >$1billion almost entirely earned off of it's back. It was without a doubt been a wildly successful product for the non-profit and to suggest otherwise is ludicrous. Likewise it continues to earn >$0.5billion/year revenue for that non-profit, to suggest that it doesn't continue to be a wildly successful product is ludicrous.
Could it have done even better for itself? Sure. Being the best possible version of yourself isn't necessary to have been successful though.