If ADP comes in below 41K today, does that actually change the Fed’s calculus given oil-driven inflation is still elevated?

Today we get ADP (forecast 41K, down from 63K last month), ISM Manufacturing PMI, and retail sales all at once. Genuinely trying to understand the transmission mechanism here.

My confusion: the standard model says weak labor data → Fed dovish → rate cut expectations rise → dollar weakens → gold up. But right now we have a competing force: oil prices elevated from the Iran war → inflation expectations sticky → Fed can't cut even if labor softens.

So my question is whether a soft ADP print today actually moves the needle on Fed policy, or whether the oil/inflation constraint makes labor data temporarily less relevant to the rate path?

Secondary question: is there precedent for a period where the Fed was simultaneously facing a supply-side inflation shock AND a softening labor market, and how did they navigate the tension between those two mandates?

Not looking for trading advice — genuinely trying to understand the theoretical framework here.