I am unsure but think it could be a very important question to answer. For example I think that maybe objecting is more about pausing a moment in time and stepping out of the situation whereas complaining we still remain “inside” the situation. Objecting can make us more detached, maybe.
Of course the example is in the court room when the barrister shouts out “objection your honor “ and then follows up with the grounds or reasoning for her objection.
I am also thinking that the objection is done in real-time, as close to now as possible whereas a complaint takes place anytime after the event. Objecting is more direct because of this but complaining can happen with anyone about anyone anywhere, like gossip, which is far more prevalent in our societies.
I think you could be right or at least I agree with you that objecting (maybe because it comes nearer to now)
has a less emotional aspect to it and more reasoning.
Objecting also seems to come before disagreeing with something/someone, and seems more about how we treat someone rather that what we say.
If the information or data we use is the digital part of the conversation and how we use it is the analog part then objecting seems to deal with more the analog part while disagreeing and ultimately complaining seems to deal with the digital part, or at least a mixture of both….maybe.