Your story reminds me of my experiences during all three of my ITs. I am also an engineering student.
The first was in school. We did all sorts of things outside the scope of what we'd call "engineering". Imagine making gari, and then calling it engineering IT because there were machines involved.
The second was completely off track, or maybe not. I worked in the technical workshop of a haulage company. I spent about two months making repairs to tractor-trailer parts. You should see me all covered in black oil; I was a beauty to behold.
Then the last, which I actually loved. I worked in an automation Academy. I learned a lot about PLCs (and programming), power systems, control systems, and electrical troubleshooting.
Like you, all the while I was on IT, I actually felt used. But at the end of it all, I am grateful I went through them. I gained a lot of practical experiences.
Indeed, what you're taught on paper is quite different from what you actually do with your hands.
Quite an interesting read.
Lol.... For real, the work pays off on the long run but it's tiring at first. How I wish these things are taught in schools.