Noted, though there is a little part of my brain that gets annoyed by routing applications insisting on using the road when the path explicitly made for cyclists is right there.

There isn't, though in person, it's more than obvious that the road is designated only for cars and the greenbelt for other users. Is there a better way to tag that for such a case?

So, if I've read it right now, I guess the right markings would be "Footpath" with the "Cycle = Yes" tag. Do I have that correct?

BYU-Idaho was my Alma Mater, so I suppose my source is personal experience. Having spent years on campus, I know the routes pretty thoroughly. Specifically, the rules at BYU-I are that bicycles are allowed everywhere on campus, with a speed limit of walking speed. Let me know if you need anything else or if I missed something!