Guiliani said his team and Sidney Powell's team have two different legal strategies. So I guess that means the two teams are pursuing their own strategies semi-independently (i.e., still coordinating their missions so they don't interfere with each other). AFAIK, Powell is pursuing a massive nationwide election fraud that is powered by a broad international conspiracy. Meanwhile, again AFAIK, Guiliani is pursuing more specific instances of election fraud, in specific Democrat-controlled cities and counties, in specific swing-states. As you can tell, I'm not a lawyer so I'm just guessing, based on what those lawyers have said, what I've watched on OAN and Newsmax, and what I've read on the web (including free republic).
And like I've frequently said, the vast majority of American voters (Republicans, Independents, and Democrats) have literally no clue that President Trump is challenging the election results, and thus they just assume Biden will be inaugurated on January 20.
You’re correct on all accounts in my opinion. Powell doing her own suits is a good thing for us. More avenues and separates the issues as you point out.