New post tracking is TBD, and hasn't been coded yet, actually. It will likely be one of the last things to go in.
It's likely to be a combination of the Classic and Threads methods - meaning that last visit timing is done completely client side via a cookie, though we'll keep track of individual thread & forum reads for the duration of your session.
The exact methods, techniques, and behavior of the feature are still subject to change.
(Full, database-level post tracking will not be making a comeback.)