Nope. If it really is FSD, there is nothing else to pay. New features are delivered with ongoing updates. All models get updates, some include new functionality that only applies to certain cars. My P85D is AP1. I received software update 2019.40.2.3, but I don't get the new games (only for MCU2-equipped cars) nor do I get advanced summon (only for AP2+ cars). However, I did get Spotify and some Navigation enhancements (recently, not necessarily in 2019.40.2.3).
Note that except for some visualizations (indicators of what the AP-computer is seeing), there are not yet any features that require HW3. When it comes time, if your car is FSD-enabled, you will be scheduled for HW3 upgrade at no charge to you. New features would come as software updates.
By the way, we are conditioned to expect software updates about once per month. The time between updates varies, but it averages about a month between.