My first experience was teaching a summer CS course for high school students. They came from around the state to the campus where I was a grad student for three weeks and we met for a total of about six hours every day. I did that for five summers and it was a great experience: very relational with small classes, but a lot of freedom and low pressure. It allowed me to get all of the standard first-time mistakes out of the way before I taught my first college classes.

I think you've hit on one of the main challenges of teaching as a profession: the good parts, like building relationships with engaged students, have to exist in a system with less-good parts, like tedious administrative work and grading. I don't have to worry about classroom control in my courses, but it's one of the hardest parts of K-12 teaching, depending on the school.

My advice is to just look for opportunities to get in the classroom (which might be virtual) and learn as you gain experience. If you are comfortable teaching in person right now, look at libraries, maker spaces, science centers, or any other public space that offers STEM-related programming. Virtual teaching can be harder (all of my classes are hybrid this semester), but there are platforms like Outschool than can allow you to offer your own small courses.