“I was wondering, this bhava asava can this also be seen as a drive to manifest an ego, to manifest oneself? A constant drive to be somebody. To be important.
Yes. One could put it that way.
Put it simply: One would have “bhava asava” as long as one has not realized the dangers in the rebirth process. That cannot be understood as long as one does not realize that one can be born in the lower four realms.