Does the renewal of the SST card also count towards the renewal of one or more of the safety trainings used to qualify for the original SST card?

No, renewing the SST card will not update/refresh the expiration date (s) of the training courses completed towards the original SST card. However, if you complete the 4-HR Supported Scaffold User and Refresher Course* as part of your SST renewal training, assuming it is the in person or virtual version of the course, you can also use that credential to comply with the worker training requirements of Local Law 52.