Is it obligatory for the giver of obligatory charity (Sadaqah/Zakah) to distribute it equally among all eight categories of recipients?

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It is not obligatory to distribute the obligatory charity to all categories listed. The Quranic verse providing the categories is meant to show those to whom it is permissible to give, not to mandate distribution to everyone, as evidenced by the fact that generalizing to every single category is not required. Allah mentioned giving charity only to the poor in one verse (Quran 2:271). The Prophet, peace be upon him, instructed Mu'adh regarding Yemen that the charity taken from the rich should be returned to the poor, mentioning only one category. Similarly, he instructed Qabisa to wait for the charity to be brought so he could order payment to him, referencing the category of debtors (Gharimin). Ali, may Allah be pleased with him, distributed funds solely to the group whose hearts are to be reconciled (Al-Mu'allafati Qulubuhum), which is a single category. These established traditions indicate that the Prophet, peace be upon him, did not believe it necessary to give every established charity to all categories, nor was he mandated to generalize the distribution among them. Rather, he would give it to whomever was readily available among those eligible.