Whether the CAC-1332 or CAC-1336 will perform better than the CAC-1333 with your Apple Studio Display is unknown to me.
I would attempt, at least snake io, to switch out the Thunderbolt cable for a standard USB cable (10 Gbps).
I would also try connecting a Thunderbolt 4 hub in between the display and the adaptor. For non-USB-C screens, it supports CAC-1336.
Thread Link: https://insights.club-3d.com/reply/re-cac-1085-needs-constant-power-cycling-to-show-image-4/