Can I downgrade my S10 to Android 11?

If you have a Galaxy S10 (or S10e / S10+) with Android 12, it won't work with Gear VR. There is a small chance that you're still able to downgrade to Android 11, but sadly it's very unlikely.

To check if your device can be downgraded, find its BIT / BINARY value.

From my research looking at the ROMs on samfw.com, it seems that your BIT has to be E or lower. In other words, if your S10 has been updated in any way since May 2022, it will have a too high BIT value to downgrade to Android 11.