What is the reason or wisdom behind the Prophet's -may Allah's peace and blessings be upon him- command to the preacher to move into the shade, and what is the ruling on that? And is the shade blessed or better than a sunny spot?

It appears that the command mentioned in the noble Hadith, regarding moving to the shade, is by way of recommendation and guidance towards what is more conducive to bodily health. This is because shade is blessed and highly beneficial for those who avoid sitting in the sun, which can activate dormant ailments. Medical books have stated that prolonged exposure to the sun is detrimental to health.