In general lay terms, "anxiety" is associated with fear-type responses, not disinterest. A lack of stress indicators would tend to indicate a lack of anxiety. A begrudging compliance when breaking through procrastination is not overcoming anxiety, but overcoming disinterest. A post-response to getting something done being "Fine, it's done, did I really have to do that?" is not indicative of overcoming fear or anxiety, because fear and anxiety are about future unknowns and would be relieved ex post facto, while procrastination still is disgruntled at having had to do it. I would present all of these as informal disagreements to blanketly equating even chronic procrastination with anxiety, as the latter tends to be understood.

Of course, that's in full acknowledgement that behavioral medicine tends to use ridiculously broad terms that tend to lead to overdiagnosis and overmedication issues we're currently dealing with (especially in schools), and they might use "anxiety" far more broadly than I am above.