Engage in modern times no longer holds any real idea surrounding power difference - you can see from the basic definition on google:
- Occupy, attract, or involve (someone's interest or attention).
- Participate or become involved in.
But it is definitely rooted in the idea. You start to see this in the 2nd and 3rd definition from Merriam Webster:
2 a obsolete : to entangle or entrap in or as if in a snare or bog b :
to attract and hold by influence or power c : to interlock with : MESH
also : to cause (mechanical parts) to mesh engage the clutch
3: to bind (someone, such as oneself) to do something especially : to
bind by a pledge to marry
The word originates from Old French Engagier, which means 'to pledge', which further brings power into the picture.
Further breaking up the word, the idea of a power difference becomes even more relevant.
The prefix 'En' starts innocently enough:
..general sense “to cause (a person or thing) to be in” the place,
condition, or state named by the stem;
But then when you consider the word 'gage', the idea of a challenge or power difference becomes even more clear.
something, as a glove, thrown down by a medieval knight in token
of challenge to combat.
Archaic. a challenge.
Archaic. a pledge or
So you could say while the word no longer carries these meanings - it certainly seems to have strong roots surrounding power differences.