So with 5.10.x-ti, TI switched to the generic SDHC layer, which is a little different then older OMAP/AM335x specific SDHC driver…
You can switch to the older v4.19.x kernel via:
sudo apt update
sudo apt install bbb.io-kernel-4.19-ti-am335x
sudo apt remove bbb.io-kernel-5.10-ti-am335x --purge
sudo reboot
and then you’ll have Bullseye with v4.19.x vs 5.10.x
Regards,