Ziehen können, nicht müssen

<div class="brett">
  <section aria-labelledby="offen-title">
    <h2 id="offen-title">Zu erledigen</h2>
    <ul class="spalte" data-name="Zu erledigen">
      <li class="karte" draggable="true">
        <span class="griff" aria-hidden="true">⠿</span>
        <span class="titel">Vertrag gegenlesen</span>
        <a href="/aufgaben/1">Details</a>
        <div class="aktionen">
          <button type="button" data-move="up"
            aria-label="Vertrag gegenlesen nach oben">Nach oben</button>
          <button type="button" data-move="down"
            aria-label="Vertrag gegenlesen nach unten">Nach unten</button>
          <button type="button" data-move="lane"
            aria-label="Vertrag gegenlesen nach Erledigt">Nach Erledigt</button>
        </div>
      </li>
      <li class="karte" draggable="true">
        <span class="griff" aria-hidden="true">⠿</span>
        <span class="titel">Angebot prüfen</span>
        <a href="/aufgaben/2">Details</a>
        <div class="aktionen">
          <button type="button" data-move="up"
            aria-label="Angebot prüfen nach oben">Nach oben</button>
          <button type="button" data-move="down"
            aria-label="Angebot prüfen nach unten">Nach unten</button>
          <button type="button" data-move="lane"
            aria-label="Angebot prüfen nach Erledigt">Nach Erledigt</button>
        </div>
      </li>
    </ul>
  </section>

  <section aria-labelledby="fertig-title">
    <h2 id="fertig-title">Erledigt</h2>
    <ul class="spalte" data-name="Erledigt"></ul>
  </section>
</div>

<p id="move-status" role="status" aria-atomic="true"></p>

JavaScript: beide Wege ändern dieselben Listen

const board = document.querySelector('.brett');
const lanes = [...board.querySelectorAll('.spalte')];
const status = document.querySelector('#move-status');
let dragged = null;

function cards(lane) {
  return [...lane.querySelectorAll(':scope > .karte')];
}

function announce(card) {
  const lane = card.parentElement;
  const rows = cards(lane);
  const title = card.querySelector('.titel').textContent;
  status.textContent = title + ': Platz ' + (rows.indexOf(card) + 1) +
    ' von ' + rows.length + ' in ' + lane.dataset.name + '.';
}

function syncControls() {
  lanes.forEach((lane, laneIndex) => {
    const rows = cards(lane);
    rows.forEach((card, index) => {
      const title = card.querySelector('.titel').textContent;
      const up = card.querySelector('[data-move="up"]');
      const down = card.querySelector('[data-move="down"]');
      up.disabled = index === 0;
      down.disabled = index === rows.length - 1;
      up.setAttribute('aria-label', title + ' nach oben');
      down.setAttribute('aria-label', title + ' nach unten');
      const laneButton = card.querySelector('[data-move="lane"]');
      laneButton.textContent = laneIndex === 0
        ? 'Nach Erledigt' : 'Nach Zu erledigen';
      laneButton.setAttribute('aria-label', title + ' ' + laneButton.textContent);
    });
  });
}

board.addEventListener('click', (event) => {
  const button = event.target.closest('button[data-move]');
  if (!button) return;
  const card = button.closest('.karte');
  const lane = card.parentElement;

  if (button.dataset.move === 'up') {
    lane.insertBefore(card, card.previousElementSibling);
  } else if (button.dataset.move === 'down') {
    lane.insertBefore(card.nextElementSibling, card);
  } else {
    const target = lanes.find((item) => item !== lane);
    target.append(card);
  }

  syncControls();
  button.focus();
  announce(card);
});

board.addEventListener('dragstart', (event) => {
  dragged = event.target.closest('.karte');
  if (!dragged) return;
  event.dataTransfer.effectAllowed = 'move';
  event.dataTransfer.setData('text/plain', '');
});

board.addEventListener('dragover', (event) => {
  if (!dragged || !event.target.closest('.spalte')) return;
  event.preventDefault();
  event.dataTransfer.dropEffect = 'move';
});

board.addEventListener('drop', (event) => {
  const lane = event.target.closest('.spalte');
  if (!dragged || !lane) return;
  event.preventDefault();
  const before = event.target.closest('.karte');
  before && before !== dragged
    ? lane.insertBefore(dragged, before)
    : lane.append(dragged);
  syncControls();
  announce(dragged);
  dragged = null;
});

board.addEventListener('dragend', () => {
  dragged = null;
});

syncControls();