Great to hear you are putting the time and effort into improving your riding; it's often that riders will blow tons of money on shiny bits for their bike but then hesitate to spend anything when it comes to rider development.
One key thing to remember is that slow is smooth and smooth is fast. While in the school, and while on track, focus on being smooth. From experience, I find that by far the best way to do this is thru your vision. Look up! Look ahead! If you are feeling panicked on track, it's likely because you're not looking far enough ahead. Your brain is reacting to what it sees in front of it RIGHT NOW instead of planning ahead. So what does this have to do with your lean angle/corner speeds and other metrics you mentioned? It's all about your comfort. You can't do anything on track without first feeling comfortable on the bike. A sure way to crash is to try to push a new skill when you haven't yet gotten comfortable with your current skill. One step at a time.
And speaking of time, there is no better riding aid other than seat time. Get as many trackdays under your belt as you can; if you ever decide to attend a KSR trackday, come see me if you'd like and I'd be more than happy to come out with you for a session to give you some pointers. I liked your comparison with University; I've made the same comparison myself with my riding. It gets frustrating when you invest the time & money and don't see the results right away. This frustration is likely what is causing your anxiety. Give it time, trust yourself, trust the school and it will come. You will have a lot of fun on the journey and likely meet some good people along the way!
??
Ride the pegs more, ride the saddle less. That will be your ah-ha! moment.