There is an interesting video purporting to show US and Syrian Government troops talking congenially at a Syrian checkpoint near Manbij. I can't see why it would be a fake and this is what professional soldiers would do ……. that is introduce themselves to each other to ensure no misunderstanding.
Pompeo is saying the US will ensure the Turks don't slaughter the Kurds in North Syria. That is one reason why the US needs to stay put. The other is Iran.