Is my prayer valid after I unintentionally moved my hands slightly and lifted them off the ground during prostration, without performing the prostration of forgetfulness (sujud al-sahw)?

The slight movement you made does not invalidate your prayer, nor does it necessitate a prostration of forgetfulness (sujood as-sahw). Excessive actions that are not part of the prayer, such as walking or scratching, invalidate the prayer, but slight ones are excused and do not require a prostration, and there is no difference between whether they were done intentionally or out of forgetfulness.