Waking at three is normal
Brief awakenings between sleep cycles are normal. What turns a two-minute waking at 3 a.m. into an hour is working out what it means.
The waking is ordinary. The alarm about it is what costs the hour.
Sleep is not one continuous thing that lasts eight hours. It moves in cycles of roughly ninety minutes, and what those cycles contain changes across the night: deep slow-wave sleep is front-loaded into the first half, REM into the second. The second half is, by design, lighter.
Brief awakenings between cycles are normal, and most of them are never remembered. Waking at three and knowing about it is not in itself a malfunction.
What turns a two-minute waking into an hour is the two minutes spent working out what it means.
What extends it is what comes next: the look at the clock, the arithmetic about how much is left, the conclusion that tomorrow is now spoiled. That is arousal, it is personally relevant, and it is precisely the machinery described in the article about effort.
It is also a different problem from falling asleep in the first place, and it deserves a different object: something that starts already quiet rather than a story that opens at full sentence length. We do not have that yet. It is on the list.
The longer answer
What to do when you can’t sleep turns this into steps for the middle of the night: stay where you are at first, don’t check the clock, and get up only if lying there has turned into a struggle. Why the night has seams in it at all is in what happens when you fall asleep, which follows the cycles that repeat roughly 4 to 6 times a night.