Do I need to have both the HDCP 1.x and HDCP 2.2 cores, or is HDCP 2.2 backward compatible with HDCP 1.x?
In order to support both HDCP 1.4 and HDCP 2.2, you will need to include both IPs in the HDMI or DisplayPort Subsystem IPs.
This is because High-bandwidth Digital Content Protection (HDCP) 1.x and 2.x are 2 different algorithms.
HDCP 2.x is a completely different link protection based on AES and is not backward compatible.
For more information, see the overview of HDCP v2.X on Wikipedia.