I agree with most of what's been said. With no governing body to define use of the term, it's akin to calling a food "lite."
In my mind, it connotes a course that's not only challenging enough for top level players, but also suitable for hosting a top level event.
A layout that's long and challenging, with legit par 4's and 5's is a good start. But a truly championship caliber course should be an example of "a course done right," and represent the game in a positive light. There's more to that than just distance and challenge.
It must have decent tees and baskets, and preferably at least porta-johns... because chit happens, and players shouldn't be forced to use leaves while chasing down the leader, or protecting a lead.
Ideally, it should also be well-maintained, but that's really more about being "tournament ready" than it is about being "championship caliber."
Ahh, but there is. PDGA has guidelines for gold (championship) courses.
Championship is often (and I think should be) used synonymously with Gold level course as defined by the PDGA: https://www.pdga.com/course-development/skill-level-guidelines