RL circuit as a feedback loop
You have written your circuit equations right and they happen to be the same as the feedback loop you have drawn. No error there. Vr really can be expressed by writing what's left of Vs when the drop in L is taken off and the drop is calculated by using Vr/R as the current of L. You can say Vr depends on what Vr happens to be and that can be presented as a feedback loop.
We can do it for everything. Let A=B/2. Thus 2A=B. It can be written as A=B-A. We cannot decide there must exist a feedback loop, no matter we could write our equation to the same form which fits to some feedback loop. For better confirmation I show what my equation presents:

The same equation is also true for the next feedback loop:

That fact gives no reason to me to start to search a hidden sensor in my voltage divider.