Except sighing isn't generally a natural response to stress, but a response to boredom. So maybe it's consciously emulating a natural behavior matching a lower

Except sighing isn't generally a natural response to stress, but a response to boredom. So maybe it's consciously emulating a natural behavior matching a lower-stress state, to help shift to that state. From personal experience, the deep inhalation preceding a sigh (extended exhalation) is also helpful.