I haven’t finished reading your whole post (though I intend to). While I like where you’re going with it in what I’ve read so far, I think you’re making a mistake.
Cold and calculating != unemotional.
Vader is clearly VERY calculating and a great tactician. He uses fear and dread to incredible effect multiple times throughout the OT (and it’s one of the reasons I think the hallway scene in Rogue One is great. It’s classic Vader tactics). And look at his whole plan to capture Luke on Bespin. Very calculated.
And I’d argue he’s very cold. Choking people to death for any failure (or daring to insult him) is cold! “Cold” is often used to infer overly harsh meanness. And that is OT Darth to a tee.
The one point from your initial argument I agree with is calm. Vader ain’t calm, he’s a total hot head who flies off the handle. But he flies off the handle in a cold and calculated manner! 😉
I read some more and I think you’re interpreting the duel in bespin all wrong. Vader clearly has a plan to wear Luke down and tempt him to the dark side. On the gantry he really turns up the heat with a brutal onslaught, but still allows Luke to back himself into a corner unscathed. Until Luke gets in ONE lucky hit on Vader’s shoulder. That changes the dynamic of the fight as now Luke is suddenly an actual potential threat to Vader and the very next thing Darth does is chop his hand off. Really, watch the fight. Vader dominates and controls the entire fight until that one moment. And as soon as Luke hits his shoulder Vader immediately chops his weapon hand off and ends the fight. That’s a VERY calculated move. And it’s exactly what a highly skilled swordsman would do.
People often use “cold” to mean “cold blooded” (Google even lists cold blooded as a synonym for cold).
Synonyms listed for cold blooded include “cruel”, “callous”, “ruthless”, “inhumane”, and “merciless”. All of which accurately describe OT Vader.