The Council of Nicaea in 325 is universally credited with fixing the rule. It did not.
What the council addressed was uniformity. A dispute had run for a century between churches that kept the resurrection on the Sunday following the Jewish Passover reckoning and those, the Quartodecimans, who kept it on 14 Nisan itself, whatever the weekday. The council's concern, as expressed in Constantine's circulating letter, was that all should keep the feast on the same day and should not depend on the Jewish calculation. No canon of Nicaea survives setting out a computational method, no equinox date, no lunar table.
The methods came afterwards, developed principally at Alexandria, and were adopted in the West only gradually and with resistance; Rome used a different table for a long time, and the British and Irish churches used another, which is what the Synod of Whitby in 664 was about.
The claim that Nicaea established the rules has an identifiable source. Dionysius Exiguus, writing in 525, asserted it, and the papal bull that promulgated the Gregorian reform in 1582 repeated it. It has been in general circulation ever since.
Eastern and Western Easter diverge because the Orthodox computation runs on the uncorrected Julian tables. The two coincide in some years and differ by one, four or five weeks in others. Proposals for a common date have been discussed repeatedly, including at Aleppo in 1997, without result. In 2025 the two happened to coincide, which is periodic rather than a settlement.