was it put somewhere on the ECAM that the plane was now in Alternate 2B law?
No, just alternate, as you have correctly observed.
The ECAM just says "Alternate", which is pretty vague.
It is not, because...
Does it matter to know if you are in alternate 1 or 2 (and the subcategory)?
...it does not if you are trying to fly the airplane. The situation might be somewhat different (and differing from reality) if one tries to promote conspiracy theories on anonymous web board. The most important information; that protections are no longer available can be perceived just by glancing the PFD, where attitude limits markings, the green "=" are replaced by yellow "x" signs.
AF447 would never have happened with better trained pilots. Period.
How do you measure quality of the training? How do you know that the fellow you are training actually understands and believes what you are telling him and is not just trying to make it through the exams and get a piece of paper unequivocally stating he is competent? How do you know that when the chips are down he won't just jettison everything he was taught and revert to some deeply rooted notion of his which might be flawed, even fatally?
Anyone finding plausible answers to these can found a consultancy business and retire a millionaire.