Incremental counting answered here depends on the grid items being in order and cannot deal with the irregular order caused by grid-auto-flow: dense and individual grid-row / grid-column.

Even if human isn't interested in pixel coordinates, script can convert them into grid indexes!

//// returnedArray[elmIdx] = {row: rowIdx, column: colIdx}
function measureGridIndexes(elms) {

  const coords = {row: [], column: []};  // The two will be very sparse arrays
  for (const [elmIdx, elm] of elms.entries()) {
    const x = elm.offsetLeft, y = elm.offsetTop;
    coords.row[y] ??= [];  // An array of element indexes at the same Y pixel coordinate
    coords.row[y].push(elmIdx);
    coords.column[x] ??= [];  // X ditto
    coords.column[x].push(elmIdx);
  }

  const gridIdxs = [];
  /// .flat() densifies a sparse array
  for (const [rowIdx, elmIdxs] of coords.row.flat(0).entries()) {
    for (const elmIdx of elmIdxs) {
      gridIdxs[elmIdx] = {row: rowIdx};
    }
  }
  for (const [colIdx, elmIdxs] of coords.column.flat(0).entries()) {
    for (const elmIdx of elmIdxs) {
      gridIdxs[elmIdx].column = colIdx;
    }
  }

  return gridIdxs;

}

Demo: https://codepen.io/phroneris/pen/RwXOJZZ

Note, however, that this code only considers integer item coordinates.

And of course, this does not address cases where the position is further customized with individual margin, position, etc.
I wish no website would do such styling, which would throw away the advantages of grid layout...