Did the people of Syria pledge allegiance to Mu'awiya at the same time people pledged allegiance to Al-Hasan, and why did Mu'awiya not pledge allegiance to Al-Hasan despite knowing of his superiority?

The people of Syria did not pledge allegiance to Mu'awiya for the Caliphate, but rather for avenging Uthman’s blood. Mu'awiya acknowledged Ali’s virtue and his rightful claim to the Caliphate, but he refrained from pledging allegiance to him until Uthman’s killers were punished. Then, Al-Hasan ceded the Caliphate to Mu'awiya in the year 41 AH, which is known as the Year of Unity (Aam al-Jama’ah).

The reason Mu'awiya refrained from pledging allegiance to Ali was their disagreement on which should take precedence: the pledge of allegiance or retribution against Uthman’s killers. Ibn Hazm stated that Mu'awiya erred by prioritizing retribution over the pledge of allegiance, but he will be rewarded for his ijtihad (independent reasoning). Ibn Taymiyyah clarified that Mu'awiya did not claim the Caliphate when he fought Ali, nor did he and his companions believe they should initiate the fighting. Rather, they saw themselves as wronged because Uthman’s killers were in Ali’s army, and they would not pledge allegiance to anyone but a Caliph capable of delivering them justice.