Not every state border crossing is an Interstate highway having controlled access. In fact, most are not (US highways, county roads, etc.).
Try walking around the nation and see how much police interaction you get :)
No, no they don't. Private property does; and controlled-access highways do; but definitely not ordinary public highways.
https://pressfreedomtracker.us/all-incidents/illinois-state-...
It's orthogonal to the general right to travel freely, but the story does demonstrate how overly broad procedural laws end up being selectively and inappropriately enforced to persecute under the color of law.