It's the short semiconscious or confused state after sleep. Very much like a hypnic jerk but you don't go back to sleep. Like waking up very early in the morning but you slept late your body is not ready to get up. Or being roused from sleep by an earthquake your body doesn't know how to react. You either get out of bed after this state or it may be followed by a short glassy-eyed idle moment.
I would call this being groggy:
not able to think or move normally because of being tired, sick, etc.
Hypnagogia is a fancy term for half-awake or half-asleep. Personally, I prefer the latter two. The Wikipedia article says:
However, hypnagogia is also regularly employed in a more general sense that covers both falling asleep and waking up […] Threshold consciousness (commonly called "half-asleep" or "half-awake", or "mind awake body asleep") describes the same mental state of someone who is moving towards sleep or wakefulness, but has not yet completed the transition. Such transitions are usually brief, but can be extended by sleep disturbance or deliberate induction, for example during meditation
This is called sleep inertia.
Sleep inertia is a physiological state characterised by a decline in motor dexterity and a subjective feeling of grogginess immediately following an abrupt awakening. - wikipedia
There is the term "sleep drunk":
having trouble coming to full wakefulness after sleep, accompanied by intense confusion and disorientation, and even sometimes violent reactions and amnesia
I would call this being drowsy:
drowsy (ˈdraʊzɪ) adj, drowsier or drowsiest
- (Physiology) heavy with sleepiness; sleepy
- inducing sleep; soporific
- sluggish or lethargic; dull
It's a metaphor, but you could try fug
It literally means a smoky atmosphere, but it can be used to mean that kind of disorientation, when you're not yet fully aware of your surroundings.