What do we know about the Council of Nicaea's ban of celebrating the Lord's Supper on the day before Passover?

There was no such edict. The Wikipedia article is confused.

The Nicene Council made only two decisions about Easter: (1) Easter should be celebrated by everyone on the same day, and (2) the date would be calculated independently of the Jewish calendar.

The details of the calculation were left to be worked out in practice, and took centuries to work out. The calculation that was eventually adopted worldwide was that of the church of Alexandria. This calculation established a Christian lunar calendar, with a Christian month of Nisan (which Christian commentators called "the month of the new" or "the first month"), a Christian Passover on its 14th day, and a Christian week of Unleavened Bread from the 15th to the 21st days. Easter was set to the Sunday in this Christian week of Unleavened Bread, that is, the third Sunday in the Christian Nisan. Or, what is saying the same thing, the Sunday after the Christian Passover on the 14th day of the lunar month. This rule was often explained by saying that if the 14th day of the Christian Nisan was a Sunday, Easter was "postponed" to the following Sunday. It is this formulation of the rule that may be the source of the false report in the Wikipedia article.

This structure of the Christian lunar calendar was modeled on the Scriptural Israelite calendar, which has the Passover on the 14th of Nisan and the Feast of Unleavened Bread on the 15th to the 21st of Nisan. Bede wrote in the 8th century that, ideally, Easter would always be on the 15th day of the lunar month. But because Easter had to be on a Sunday, one of the other days of Unleavened Bread sometimes had to be chosen. "Nevertheless", he wrote, "it never happens that our paschal solemnity fails to embrace some one of the days of the legal Passover." De Temporum Ratione 59.

Upon closer inspection it became evident that the discussion of "the Lord's Supper" is referred to in discussion under the term "Easter" because the Roman bishops and Constantine were intent on establishing Easter as a uniform Christian feast distinct from simply a redefinition of the Passover and to move from the OT Hebrew calendar to a date based on the solar Julian calendar. Eusebius' writings seethe with anti-Jewish ranting and drip with honeyed words about Constantine, and calls for complete obedience to orders from Rome:

Eusebius, in The Life of Constantine Book III reports (emphases via bolding mine):

Chapter 18. He speaks of their Unanimity respecting the Feast of Easter, and against the Practice of the Jews. At this meeting the question concerning the most holy day of Easter was discussed, and it was resolved by the united judgment of all present, that this feast ought to be kept by all and in every place on one and the same day. For what can be more becoming or honorable to us than that this feast from which we date our hopes of immortality, should be observed unfailingly by all alike, according to one ascertained order and arrangement? And first of all, it appeared an unworthy thing that in the celebration of this most holy feast we should follow the practice of the Jews, who have impiously defiled their hands with enormous sin, and are, therefore, deservedly afflicted with blindness of soul. For we have it in our power, if we abandon their custom, to prolong the due observance of this ordinance to future ages, by a truer order, which we have preserved from the very day of the passion until the present time. Let us then have nothing in common with the detestable Jewish crowd; for we have received from our Saviour a different way. A course at once legitimate and honorable lies open to our most holy religion. Beloved brethren, let us with one consent adopt this course, and withdraw ourselves from all participation in their baseness. For their boast is absurd indeed, that it is not in our power without instruction from them to observe these things. For how should they be capable of forming a sound judgment, who, since their parricidal guilt in slaying their Lord, have been subject to the direction, not of reason, but of ungoverned passion, and are swayed by every impulse of the mad spirit that is in them? Hence it is that on this point as well as others they have no perception of the truth, so that, being altogether ignorant of the true adjustment of this question, they sometimes celebrate Easter twice in the same year. Why then should we follow those who are confessedly in grievous error? Surely we shall never consent to keep this feast a second time in the same year. But supposing these reasons were not of sufficient weight, still it would be incumbent on your Sagacities to strive and pray continually that the purity of your souls may not seem in anything to be sullied by fellowship with the customs of these most wicked men. We must consider, too, that a discordant judgment in a case of such importance, and respecting such religious festival, is wrong. For our Saviour has left us one feast in commemoration of the day of our deliverance, I mean the day of his most holy passion; and he has willed that his Catholic Church should be one, the members of which, however scattered in many and diverse places, are yet cherished by one pervading spirit, that is, by the will of God. And let your Holinesses' sagacity reflect how grievous and scandalous it is that on the self-same days some should be engaged in fasting, others in festive enjoyment; and again, that after the days of Easter some should be present at banquets and amus*m*nts, while others are fulfilling the appointed fasts. It is, then, plainly the will of Divine Providence (as I suppose you all clearly see), that this usage should receive fitting correction, and be reduced to one uniform rule.

Chapter 19. Exhortation to follow the Example of the Greater Part of the World. Since, therefore, it was needful that this matter should be rectified, so that we might have nothing in common with that nation of parricides who slew their Lord: and since that arrangement is consistent with propriety which is observed by all the churches of the western, southern, and northern parts of the world, and by some of the eastern also: for these reasons all are unanimous on this present occasion in thinking it worthy of adoption. And I myself have undertaken that this decision should meet with the approval of your Sagacities, in the hope that your Wisdoms will gladly admit that practice which is observed at once in the city of Rome, and in Africa; throughout Italy, and in Egypt, in Spain, the Gauls, Britain, Libya, and the whole of Greece; in the dioceses of Asia and Pontus, and in Cilicia, with entire unity of judgment. And you will consider not only that the number of churches is far greater in the regions I have enumerated than in any other, but also that it is most fitting that all should unite in desiring that which sound reason appears to demand, and in avoiding all participation in the perjured conduct of the Jews. In fine, that I may express my meaning in as few words as possible, it has been determined by the common judgment of all, that the most holy feast of Easter should be kept on one and the same day. For on the one hand a discrepancy of opinion on so sacred a question is unbecoming, and on the other it is surely best to act on a decision which is free from strange folly and error.

Chapter 20. Exhortation to obey the Decrees of the Council. Receive, then, with all willingness this truly Divine injunction, and regard it as in truth the gift of God. For whatever is determined in the holy assemblies of the bishops is to be regarded as indicative of the Divine will. As soon, therefore, as you have communicated these proceedings to all our beloved brethren, you are bound from that time forward to adopt for yourselves, and to enjoin on others the arrangement above mentioned, and the due observance of this most sacred day; that whenever I come into the presence of your love, which I have long desired, I may have it in my power to celebrate the holy feast with you on the same day, and may rejoice with you on all accounts, when I behold the cruel power of Satan removed by Divine aid through the agency of our endeavors, while your faith, and peace, and concord everywhere flourish. God preserve you, beloved brethren!

The emperor transmitted a faithful copy of this letter to every province, wherein they who read it might discern as in a mirror the pure sincerity of his thoughts, and of his piety toward God.

Of late there appears to be a great deal of interest in restoring the biblical calendar to Protestant and "Messianic Jewish" practices:

When is Passover - Learning Yahweh's Calendar - Assembly of Yawheh in North Alabama

Creator's Calendar - 119ministries.com

What remains an open question to me is when the annual Passover-based celebration of the Lord's Supper changed to one every Sunday. Apparently it was after the First Ecumenical Council of Nicaea, yes?

We know there was a conflict in the very early church about the 3-day observance of Christ's death, burial, and resurrection. Some wanted to observe the 14th (Passover), which came to be called the Last Supper. Others wanted to observe the resurrection, which came to be determined about Sunday sunrise. The Council of Nicea met to discuss the issue, among other issues. They decided that overlapping observances was to be avoided. Constantine was the guarantee. Here is his letter to the churches.

When the question relative to the sacred festival of Easter arose, it was universally thought that it would be convenient that all should keep the feast on one day; for what could be more beautiful and more desirable, than to see this festival, through which we receive the hope of immortality, celebrated by all with one accord, and in the same manner? It was declared to be particularly unworthy for this, the holiest of all festivals, to follow the custom [the calculation] of the Jews, who had soiled their hands with the most fearful of crimes, and whose minds were blinded. In rejecting their custom,113 we may transmit to our descendants the legitimate mode of celebrating Easter, which we have observed from the time of the Saviour’s Passion to the present day [according to the day of the week]. https://ccel.org/ccel/schaff/npnf214/npnf214.vii.x.html

So again, their goal was to observe a resurrection feast for all the churches on the same day. At the same time, the goal was to avoid said feast on the same day as Passover or Unleavened Bread. The difference would be to observe the feast on a day of the week (Sunday), rather than on a date as determined from Scripture (the 14th Passover). The decision was made therefore to observe Easter on the first Sunday following the first full moon (the full moon was typically the first day of the Feast of Unleavened Bread) after the Spring Equinox.