The sleep and behaviour link is strong, and the direction is not settled
That short sleep is associated with irritability, poorer attention and more conflict is among the better-supported findings in child development. It is repeatedly reported as though the causal arrow were established.
What the studies mostly are
Largely observational and frequently based on parent-reported sleep, which correlates imperfectly with measured sleep. Families under stress report both worse sleep and worse behaviour, and stress plausibly causes both.
Where it is firmer
Experimental work that restricts or extends sleep by an hour in otherwise typical children does find changes in mood and attention within days. That is a real causal signal, in one direction, at a dose most families can act on.
An hour earlier is a bigger intervention than it sounds, and one of the few with evidence behind it.
The honest summary
Protecting sleep is worth doing and likely to help. Attributing a specific difficult week to a specific bedtime drift is a story, not a measurement.