MongoDB Aggregation : How to compare among array of objects in same document

This may not be exactly what the OP is looking for but the challenge of iterating over a list and examining each element in the context of the rest of the list is a good one. Here’s a potential solution:

//  The end date of one object should not be between another's start and end date – 

c = db.foo.aggregate([
  {
    $project: {
    SKUPromo: {
        /*
          This is the pseudocode in regular javascript:
          len = SKUPromo.length;
          for(n = 0; n < len; n++) {
            targ = SKUPromo[n]
            for(m = 0; m < len; m++) {
              if(n == m) {  continue }
              if(targ.enddate < SKUPromo[m].enddate and targ.enddate > SKUPromo[m].startdate
                    idmap[targ._id].append(m);
              }
            }
          }
        */

        // Iterate over SKUPromo and call each one 'targ':
        $map: {input: "$SKUPromo", as: "targ", in: {

        // Now run a reduce over SKUPromo to assess against 'targ'.
        // The $mergeObjects is there to add the overlaps field
        // to the existing 'targ'.  In pipeline logic we cannot say:
        //    targ['overlaps'] = some_list
        // instead we must say:
        //    $mergeObjects: [ '$$targ', {overlaps: some_list}]
        //
        
              $mergeObjects: ["$$targ",
                {overlaps: {
                  $reduce: {input: "$SKUPromo",
                    initialValue: [],
                    in: {
                      $cond: [
                        { // IF
                          $and: [
                            { $ne: ["$$targ", "$$this"] },
                            { $lt: ["$$targ.endDateTime", "$$this.endDateTime"] },
                            { $gt: ["$$targ.endDateTime", "$$this.startDateTime"] }
                          ]
                        },
                        { $concatArrays: ["$$value", ["$$this._id"]] }, // THEN
                        "$$value" // ELSE
                      ]
                    }
                  }
                }
              }
            ]
          }
        }
      }
    }
  }
    // Only keep things with anything in the overlaps array:
    ,{$project: {
      overlaps: {
        $filter: {
          input: "$SKUPromo",
          as: "targ",
          cond: { $ne: ["$$targ.overlaps", []] }
        }
      }
    }
  }

]);

This yields:

{
  _id: '2531090',
  overlaps: [
    {
      _id: '3',
      startDateTime: ISODate("2023-06-25T05:00:00.000Z"),
      endDateTime: ISODate("2023-07-02T04:59:59.000Z"),
      promotionID: '8749',
      skuId: '2531090',
      overlaps: [
        '2'
      ]
    },
    {
      _id: '5',
      startDateTime: ISODate("2023-01-01T06:00:00.000Z"),
      endDateTime: ISODate("2023-01-07T05:59:59.000Z"),
      promotionID: '6262',
      skuId: '2531090',
      overlaps: [
        '1'
      ]
    }
  ]
}