

Exactly. If you’re apologizing, apologize. There’s nothing wrong with also asking to have a conversation about what caused the conflict.
“I’m sorry” and "can we talk about what happened?” are both valid, but ultimately aren’t dependent on each other.
Management isn’t your friend, but managers are still people. The job is not the person. A good, nice, friendly person can have a job where their work interests aren’t necessarily aligned with yours and still try to do what they can to see that your interests are met.
That’s just not true. It’s not universally untrue, but it’s just wrong to default to such an antagonistic view from the outset.
All that to say: it sounds like you’re mainly having difficulty reconciling your thoughts on how you behave towards people with how you behave towards management. If you replace job related words with words like “people” or “person” then the question gets a lot easier.
It’s pretty obvious to me that you apologize. Then ask if they’d be open to a conversation about what you feel could have gone better.
“Hey, do you have a minute? Sorry about how I acted when we were talking the other day. I thought about it and realized that I hadn’t been listening, which wasn’t right of me and made things worse. Would you be open to discussing it now that we have a little distance from it? I’d like to explain myself a bit and share some related concerns that I had, if nows a good time.”
They’re a person. If you feel your wronged them, apologize. If you feel like you want to explain things and offer feedback, just make it clear this isn’t a prerequisite for the apology or anything.