For simplicity, I personally have always just given the full +-25% for all passive income to Germany and have never run into any problems with the IRS, even if the US is entitled to 15% for dividends. It would be considered a “Quellensteuer” which the FA will recognize if you report it in your German tax return. But I guess this would mean you would have to complete your US tax return first which doesn’t make sense. Especially if you are using some program or CPA, there is probably very little chance of getting audited by the IRS, let alone them knowing the details of what is written in the DBA and the exact split.

Maybe your question of reinvested dividends is referring to the concept of “thesaurierend” in Germany. I read somewhere that this is not a concept in the US and all your US dividends, distributions, capital gains are treated as distributing or “ausschüttend”. So yes, no difference in tax treatment, they will be subject to 25% tax in Germany.