Thanks for the detailed info.
I wonder how much that curriculum has evolved over the last two decades, since the advent of the UFC. Prior to that time I had seen (in books, demos, videos, and from visiting classes) plenty of stand-up grappling (throws, armlocks, and wristlocks) from practitioners of Karate and TKD, but exactly zero ground grappling. No mount/side mount/guard. No leglocks on the ground. None of that. The closest would be techniques where the karateka would be standing or kneeling over a downed opponent while applying a submission.
This matches what I was taught in the 70's in TKD dojangs. Plenty of joint locks, throws, takedowns, etc. But no rolling on the ground.