NVIDIA's website lists 566.03 as the newest "Game Ready" driver, and 565.90 as the newest "Studio" driver. Does the Studio driver contain the security fix as well?
No. The hotfix is in v566 or later. The "Game" and "Studio" drivers are widely believed to be from one codebase, just released on different schedules and with a larger test suite for the "Studio" driver. So you have your choice of hotfix-without-testing or tested-without-hotfix!