The point is just that certain kinds of self-theories can be ruled out through a jhāna experience. The full recognition of anattā is deeper.
You are quite right. No awareness of selfhood is not a sufficient premise to claim there is no self. In fact, there are countless times during a day when one is fully occupied with what one is doing and there is no awareness of a self. Yet it is clear enough that one cannot make any non-self claim on that basis. This is also true for a deep state of samādhi. The sense of self is completely gone, yet it returns when one emerges, usually taking the very state of samādhi as its object. The point, rather, is that the experience of a deep state of samādhi will enable one to exclude certain aspects of personality as a self. This includes the five senses and the will. For a full insight into anattā one will have to go even deeper. But it’s a good start!
In Buddhism tradition and experience go hand in hand. In fact, it is precisely the fact that Buddhism is a living tradition that makes it so interesting to many. The insights of early Buddhism are still being had in the present day.
From my perspective you have not had a jhāna experience.