Birtherism was just the usual conspiracy theory nonsense.
And Trump rode that nonsense for longer than any other public figure in the US.
It had nothing to do with Obama's race, or the fact that he might be "un-American." It only had to do with the fact that there were loose ends that Obama (probably as part of a deliberate strategy) refused to tie down.
That is just it: there were no loose ends.
And Trump latched on to birtherism in the same way that an Alex Jones latched on to 9/11 trutherism. It was a way to attract attention to himself and nothing more.
And nothing less.