Hello Krileon,
As I made many test and changes, I restarted from scratch joomla install as well CB , CB actions ...etc..
understanding your explanations ( I think ), I had the idea for trouble shooting to change the action itself and get out of PHP considerations.
I have now configured the following :
Action type : Email
User , switched from automatic to User
Trigger : onafterloginsuccess
in the action tab ( so email ) :
Subject : TEST Login
body :
this is the email :