I was wondering how long I have until I have to take a APFT (or if I am to take a diagnostic)?

When your profile ended in June, that is when you were able to take an APFT. You could have taken one any time between June and now. You could very well take an APFT on your next BTA weekend. Get with your NCO(s) to know for certain as they should be keeping you up to date about this.

The publication you are looking for is FM 7-22 (ARMY PHYSICAL READINESS TRAINING)

I think it would be the next opportunity, so if you are reserves and have BA in two weeks it would be then.
Have you asked your First Line Leader? They would be a good beginning resource so they can fill you in as well as track any necessary training you may have coming.

Did none of your medical staff or command explain this to you? The way it works is that while you are on profile you can take an APFT up to the limitations listed on the profile. Your profiles includes the heal time as well as the recuperation time so that at the end of your profile you command can have you take a full, for record APFT as you should be up to minimal Army standards. The fact that they have not given you one yet is a blessing. Just get in shape and wait for them to administer it.