This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F629 offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character βweary faceβ for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: crying, face, fail, feels, hungry, mad, nooo, sad, sleepy, tired, unhappy, weary.
On Youtube this character is sometimes wrongly displayed as U0001f629.
The Wikipedia has the following information about this codepoint:
Fatigue describes a state of tiredness (which is not sleepiness), exhaustion or loss of energy.
Fatigue (in the medical sense) is sometimes associated with medical conditions including autoimmune disease, organ failure, chronic pain conditions, mood disorders, heart disease, infectious diseases, and post-infectious-disease states. However fatigue is complex and in up to a third of primary care cases no medical or psychiatric diagnosis is found.
Fatigue (in the general usage sense of normal tiredness) often follows prolonged physical or mental activity. Physical fatigue results from muscle fatigue brought about by intense physical activity. Mental fatigue results from prolonged periods of cognitive activity which impairs cognitive ability, can manifest as sleepiness, lethargy, or directed attention fatigue, and can also impair physical performance.