Thank you for that question. There isn't a simple answer. I'll try to make it as simple as I can.
The convention, the STCW that you refer to, has just recently had an additional protocol, and Transport Canada has implemented amended regulations to reflect the changes in that protocol to STCW. The enforcement of that convention with the additional protocol is the responsibility of Transport Canada, which it does through its inspection regime and/or class societies, depending on which regulation it is. I have confidence that it is being achieved.
I think your question also asks if part of that is related to safety management systems. From my understanding of it, it is not at this point. STCW deals primarily with the certification of people and their capabilities and the standards of their employment in ships.