Is it permissible to delay Fajr prayer or to perform tayammum for it if waking up or performing ablution at its prescribed time would harm the worshiper's health and affect their sleep and daily activity, knowing that this harm is not due to the difficulty of waking up, but rather due to the short night and the effect of ablution on the sleep cycle?

It is not permissible to delay the Fajr prayer or any other prayer beyond its legally prescribed time without a legitimate Shar'i excuse. What the questioner mentioned is not an excuse for delaying the prayer or for resorting to Tayammum (definition) instead of Wudu'. One must maintain the Fajr prayer at its appointed time and perform Wudu' for it, for that does not impede blood circulation nor harm the body. What was mentioned may be from the whispers of Satan to discourage you from prayer, so beware of that, and remember His Almighty's saying: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing" (An-Nur: 21).