Has it been authentically reported from the Prophet, peace and blessings be upon him, that he said: "If I were to make anything obligatory upon my Ummah after the prayer, it would be the beard and the Siwak," and can this be used to argue against the obligation of letting the beard grow?

We do not know of anything in the Sunnah of the Prophet regarding the obligation of using the miswak before every prayer for the sake of the beard. Rather, it was narrated from the Prophet, may Allah's prayers and peace be upon him: "Were it not that I would overburden my Ummah, I would have commanded them to use the miswak with every prayer." This is evidence that using the miswak is not obligatory. Al-Nawawi and Ibn Qudamah reported the consensus of scholars that using the miswak is a Sunnah and not obligatory, except for what was narrated from Dawud and Ishaq regarding its obligation, which is an incorrect narration attributed to them. As for the beard, the Prophet, may Allah's prayers and peace be upon him, commanded its growth in well-known hadiths.