I do not know if the procedure has changed with the switch from the GOES to the TTP website. I also don't know if the procedure is the same or different for US citizens and lawful permanent residents than for citizens of other countries who are not US LPR's; however, when I received my conditional approval a few years ago, I received an email notification that there was a change in the status of my application and that I needed to login for more information.

It may help peruse one of the threads discussing GE for UK based applicants. There is one in the Trusted Travelers forum and another in the USA forum. OK, I just searched the latter. There are several posts going back to 2015 stating that the members received email notifications when their application status changed from "Pending Review" to "Conditional Approval."