For anyone else going down this path, power/control:auto is the default behavior for the card on Mint.
This was being overwritten on my computer by tlp, which sets power/control:on for all pcie devices by default when on AC power, but auto only on battery power. This is controlled by the RUNTIME_PM_ON_AC parameter in /etc/tlp.conf. It’s not clear to me why the GPU wasn’t sleeping while on battery power before, but I see that it is sleeping properly now.
Relevant docs: Power Consumption — TLP 1.6 documentation
Thank you for your help!