SUGGESTION

Perhaps you can use a Custom Google Sheet Function (=findOverlaps()) using a script to mimic the ARRAYFORMULA behaviour. You may check this sample script below that you can add as a bound script in your spreadsheet file:

Follow this quick guide on how to add a bound script in your spreadsheet.

Custom Function Script

function findOverlaps(arr) {
  var res = [];
  var filtered = arr.filter((data,index)=>{
                 return data[2] == arr.map((data)=>{return data[2]}).filter((a, i, aa) => aa.indexOf(a) === i && aa.lastIndexOf(a) !== i) ? data.push((parseInt(index)+1)) : null;
  });

  filtered.map((data,index)=>{
    for(var x=0; x < 2; x++){
      filtered.map((check)=>{
        res.push([arr.map((data)=>{return data[2]}).filter((a, i, aa) => aa.indexOf(a) === i && aa.lastIndexOf(a) !== i).join(''),data[3],dateRangeOverlaps((filtered[parseInt(index)][x]),check[0],check[1], check[3])]);
      });
    }
  });

  res = res.filter((z)=>{return z[0] == 'Task1' && z[2] != 'x' ? z[2] : ''});

  return arr.map((x,index)=>{
    return res.map((look)=>{
      if((parseInt(index)+1) == look[1]){
        return "Row"+look[2];
      }
    }).filter((fn)=>{return fn}).join(', ')
  });

}

function dateRangeOverlaps(currentDateToCheck, startDate, endDate, row) {
    return (currentDateToCheck > startDate && currentDateToCheck < endDate) ? row : 'x'
}

Demonstration

See this sample: