To answer your main question, no, I don’t believe for a second that you are manipulating your child. If you were trying to manipulate him, I’m pretty sure you’d know it! You sound like an objective and level-headed person, and the fact that you’re open to criticism and adapting where necessary shows that you only want the best for your kid, not trying to get your own way or stroke your ego.
I take a very similar approach with disciplining my 3yo (almost 4), though I often slip up getting angry and frustrated.. Eek. I think the important thing is just ensuring your child understands the cause+consequence dynamic, and the idea of separating the behaviour from the child himself being bad is key, as you mention. As long as the discipline or conflict ends on a positive with reinforcing that you love them, with you child also giving you positive feedback, then it’s healthy discipline in my opinion — even if every step along the way may look different for different people/personalities.
Couples can have slightly different styles and that’s fine as long as you can agree on the same basic principles and outcomes.
Hope that helps!