I would not recommend using an application's Application Support folder to store other stuff - not in general, and not unless it is specifically supported in some way (like maybe BBEdit says to put your scripts there or something like that).
That's an internal detail of the app that could change and who knows the consequence and the developer isn't necessarily going to think about the consequences to stuff that has been added (which includes me in two years when I've forgotten this thread).
So yes, it is better to put it in the Documents folder, or otherwise in your home folder somewhere.
@ccstone’s layout looks good, but of course it gets to be a long path. Clear, but long.