Being so exhausted, usually sleepy or drunk to the point of mental disorientation, and uncoordinatedness. One can be grogged out awake mostly. It can mean to be in a deep sleep after one was very tired, but the is the second meaning.
Definition: an expression of unequivocal poggers, in a groggers way
Deriving from the name of one of Anilist's most influential reviewers, groggy1, known for popularizing the avant-garde Gakuen Handsome.