Google Sheet: DoRangesHaveOverlap() = do all of these ranges have shared overlap points? GetRangeUnion() = return the union of any number of ranges

DoRangesHaveOverlap.gs

/**
 * @param {SpreadsheetApp.Range} ranges
 * @returns {boolean}
 * - `true` indicates all ranges share the same overlapping point(s) with all others
 * - `false` indicates no shared overlap point, even if they all overlap individually
 */
function DoRangesHaveOverlap(...ranges) {
  return GetRangeUnion(...ranges) !== null;
}

Example_IsUnion.gs

function Example_IsUnion() {
  const sheet = SpreadsheetApp.getActiveSheet();
  const ranges = [
    sheet.getRange(5, 5, 4, 4),
    sheet.getRange(6, 6, 4, 4),
    sheet.getRange(7, 7, 4, 4),
  ];
  // ranges.forEach((range) => Logger.log("range: %s", range.getA1Notation()));

  const sharedOverlap = DoRangesHaveOverlap(...ranges);
  Logger.log("sharedOverlap: %s", sharedOverlap);

  const union = GetRangeUnion(...ranges);
  Logger.log("union: %s", union?.getA1Notation());
}

// sharedOverlap: true
// union: G7:H8

Example_NoUnion.gs

function Example_NoUnion() {
  const sheet = SpreadsheetApp.getActiveSheet();
  const ranges = [
    sheet.getRange(4, 4, 4, 4),
    sheet.getRange(5, 5, 4, 4),
    sheet.getRange(6, 6, 4, 4),
    sheet.getRange(7, 7, 4, 4),
    sheet.getRange(8, 8, 4, 4),
  ];
  // ranges.forEach((range) => Logger.log("range: %s", range.getA1Notation()));

  const sharedOverlap = DoRangesHaveOverlap(...ranges);
  Logger.log("sharedOverlap: %s", sharedOverlap);

  const union = GetRangeUnion(...ranges);
  Logger.log("union: %s", union?.getA1Notation());
}

// sharedOverlap: false
// union: null

GetRangeUnion.gs

 * @param {SpreadsheetApp.Range[]} ranges
 * @returns {SpreadsheetApp.Range}
 */
function GetRangeUnion(...ranges) {
  const unionPair = (rangeA, rangeB) => {
    const union = {
      left: -1,
      right: -1,
      top: -1,
      bottom: -1,
    };

    // if
    //   both range's left edge is at/before both range's right edge
    // then
    //   union.left  is the rightest left  side
    //   union.right is the leftest  right side
    if (
      rangeA.getColumn() <= rangeB.getLastColumn() && // rangeA's left edge is at/before rangeB's right edge
      rangeB.getColumn() <= rangeA.getLastColumn()    // rangeB's left edge is at/before rangeA's right edge
    ) {
      union.left  = Math.max(rangeA.getColumn()    , rangeB.getColumn()    ); // left  is the rightest left  side
      union.right = Math.min(rangeA.getLastColumn(), rangeB.getLastColumn()); // right is the leftest  right side
    }

    // if
    //   both range's top edge is at/above both range's bottom edge
    // then
    //   union.top    is the bottomest top    side
    //   union.bottom is the toppest   bottom side
    if (
      rangeA.getRow() <= rangeB.getLastRow() && // rangeA's top edge is at/before rangeB's bottom edge
      rangeB.getRow() <= rangeA.getLastRow()    // rangeB's top edge is at/before rangeA's bottom edge
    ) {
      union.top    = Math.max(rangeA.getRow()    , rangeB.getRow()    ); // top    is the bottomest top    side
      union.bottom = Math.min(rangeA.getLastRow(), rangeB.getLastRow()); // bottom is the toppest   bottom side
    }

    if (
      union.left   < 0 ||
      union.right  < 0 ||
      union.top    < 0 ||
      union.bottom < 0    
    ) return null; // no union occurred.

    return rangeA.getSheet().getRange(union.top, union.left, union.bottom-union.top+1, union.right-union.left+1);
  };

  return ranges.reduce((rangeA, rangeB) => unionPair(rangeA, rangeB));
}