01make-pair-v2.css

#players-input {
  box-sizing: border-box;
  width: 100%;
  max-width: 600px;
  height: 200px;
  padding: 4px;
  resize: vertical;
}
#pair-select {
  height: 2em;
}
.settings {
  display: flex;
  flex-direction: column;
  row-gap: 16px;
  margin: 12px 0;
}
.settings__row {
  display: flex;
  gap: 12px;
}
#result {
  display: flex;
  flex-direction: column;
  row-gap: 12px;
  margin: 24px 0;
}
.result__block {
  padding: 12px;
  border: 1px solid #aaa;
  border-radius: 8px;
  overflow-x: auto;
}
.result-table {
  margin-top: 4px;
  border-collapse: collapse;
}
.result-table__cell {
  padding: 4px 8px;
  border: 1px solid #71ab09;
}

02make-pair-v2.html

<textarea
  id="players-input"
  placeholder="Aさん
Bさん
Cさん
Dさん
Eさん
Fさん"
></textarea>
<div class="settings">
  <div class="settings__row">
    <select id="pair-select">
      <option value="once">同じ組み合わせのペアを許可する</option>
      <option value="all" selected>
        同じ組み合わせのペアを許可しない
      </option>
    </select>
  </div>
  <div class="settings__row">
    <button id="submit-bt">ペア分けを決める</button>
    <button id="reset-bt">リセット</button>
  </div>
</div>
<div id="result"></div>

03make-pair-v2.js

const nowloading = new nowLoading();
nowloading.start();

const playersInput = document.getElementById('players-input');
const pairSelect = document.getElementById('pair-select');
const result = document.getElementById('result');
let roundNumber = 1;

init();

function init() {
  const submitBt = document.getElementById('submit-bt');
  const resetBt = document.getElementById('reset-bt');
  playersInput.addEventListener('input', () => {
    roundNumber = 1;
    result.textContent = '';
  });
  pairSelect.addEventListener('change', () => {
    roundNumber = 1;
    result.textContent = '';
  });
  submitBt.addEventListener('click', submitHandle);
  resetBt.addEventListener('click', () => {
    roundNumber = 1;
    result.textContent = '';
  });
  //
  playersInput.value =
    'Aさん\nBさん\nCさん\nDさん\nEさん\nFさん\nGさん\nHさん';
  nowloading.stop();
}

function submitHandle() {
  nowloading.start();
  if (pairSelect.value === 'once') {
    listUpOnce();
  } else if (pairSelect.value === 'all') {
    result.textContent = '';
    listUpAll();
  }
  nowloading.stop();
}

function getPlayersList() {
  return playersInput.value
    .split(/\n/)
    .map((v) => v.trim())
    .filter((v) => v !== '');
}

function writeResultBlock(pairList, roundIndex) {
  const block = document.createElement('div');
  block.classList.add('result__block');
  const title = document.createElement('div');
  title.classList.add('result__block__title');
  title.textContent = `ペア分け結果 ${roundIndex}回目`;
  block.appendChild(title);
  const table = document.createElement('table');
  table.classList.add('result-table');
  pairList.forEach((pair) => {
    const tr = document.createElement('tr');
    pair.forEach((player) => {
      const td = document.createElement('td');
      td.classList.add('result-table__cell');
      td.textContent = player || '';
      tr.appendChild(td);
    });
    table.appendChild(tr);
  });
  block.appendChild(table);
  return block;
}

function listUpOnce() {
  const players = getPlayersList();
  if (players.length === 0) return;
  shuffle(players);
  if (players.length % 2 === 1) players.push(undefined);
  const pairList = splitArray(players, 2);
  const block = writeResultBlock(pairList, roundNumber);
  result.prepend(block);
  roundNumber++;
  //
  function splitArray(array, size) {
    return array.flatMap((_, i, a) =>
      i % size ? [] : [array.slice(i, i + size)]
    );
  }
}

function listUpAll() {
  const players = getPlayersList();
  if (players.length === 0) return;
  shuffle(players);
  if (players.length % 2 === 1) {
    players.push(undefined);
  }
  const playerLength = players.length;
  const roundMax = playerLength - 1;
  const pairMax = Math.ceil(playerLength / 2);
  for (let round = 0; round < roundMax; round++) {
    const lastChild = players.slice(-1);
    const roundPlayerList = players
      .slice(round, playerLength - 1)
      .concat(players.slice(0, round))
      .concat(lastChild);
    const pairList = [];
    for (let pIndex = playerLength / 2 - 1; pIndex >= 0; pIndex--) {
      const pair = [
        roundPlayerList[pIndex],
        roundPlayerList[playerLength - 1 - pIndex],
      ];
      pairList.push(pair);
    }
    const block = writeResultBlock(pairList, round + 1);
    result.appendChild(block);
  }
}

function randomMN(m, n) {
  const d = Math.max(m, n) - Math.min(m, n);
  return Math.floor(Math.random() * (d + 1) + Math.min(m, n));
}

function shuffle(array) {
  for (let i = array.length - 1; i >= 1; i--) {
    const j = randomMN(0, i);
    [array[j], array[i]] = [array[i], array[j]];
  }
}