How fast do oil shock spillover effects feed into core PCE inflation?

Headline PCE recently climbed to 3.5%, up from 2.8% back in February.
Core PCE also ticked higher, moving from 3.0% to 3.2% in the same window.

The direct link between crude prices and headline inflation is pretty straightforward.
Higher oil immediately lifts gasoline, utility costs and overall transportation expenses.

What I’m curious about is core PCE.
Core inflation strips out food and energy entirely, so direct oil impacts don’t count here.
That makes this recent core uptick far more notable.

I want to break down the real transmission speed and secondary spillover channels.

How quickly do second-round effects from a major oil shock show up in core inflation?
The key channels I can identify:
rising transport and production input costs forcing businesses to hike prices,
broad service cost adjustments,
higher headline inflation pushing wage bargaining pressure,
and shrinking profit margins that force firms to pass cost hikes to consumers.

Is this two-month core PCE increase in line with historical oil shock patterns?
Or does this quick uptick signal broader inflation pressure, beyond just energy-driven costs?

Are there well-documented historical cases economists use, to separate direct energy inflation from those delayed second-round spillover effects?

Not looking for trading takes or market forecasts.
Just trying to fully understand how supply-side energy shocks bleed into broader inflation metrics.