How did the Prophet (peace be upon him) retract an eschatological matter, such as the glad tidings of Paradise, as mentioned in the hadith of Abu Hurayrah, in the face of 'Umar ibn Al-Khattab's objection? And was that retraction with God's permission, or was the giving of glad tidings not a revelation?

What was mentioned is not a retraction of the ruling, but rather a delay in announcing it, out of consideration for a benefit. Indeed, it is permissible for a scholar to remain silent about a matter if he fears mischief from it. The Prophet, peace and blessings be upon him, specifically taught his companions certain knowledge, excluding the general public, fearing their lack of understanding or their reliance on it, as in the Hadith (definition) of Mu'adh: "I fear that they might rely on it." The Prophet, peace and blessings be upon him, also agreed with Al-Abbas in exempting idhkir from the prohibition of Mecca. Similarly, 'Umar prevented Mu'adh from giving glad tidings to the people lest they rely on it, and the Prophet, peace and blessings be upon him, approved of that, which is counted among 'Umar's موافقات (concordances).