Please try the following:
1. In each parts sheet, select cell A1 and under Alignment, unselect Wrap Text (needed for proper formatting by the code).
2. Delete any worksheets other than the parts sheets and the product index sheet. If this is not desirable, a code adjustment will be needed.
3. Replace the product index Worksheet_Activate code with the following:

Private Sub Worksheet_Activate()
Dim sh As Worksheet, rw As Long, endrw As Long, OMRw As Long

    If MsgBox("Rebuild Parts Index?", vbYesNo, "Parts Index") <> vbYes Then Exit Sub
    
    Application.ScreenUpdating = False
    rw = Cells.SpecialCells(xlCellTypeLastCell).Row
    Rows("2:" & rw).Delete
    OMRw = 2
    For Each sh In ActiveWorkbook.Sheets
        With sh
            If .Name <> ActiveSheet.Name Then
                If .Range("E" & .Rows.Count).End(xlUp).Row > 2 Then ' There are included parts on this sheet
                    .Range("A1").Copy Cells(OMRw, 1) ' Section name
                    Range(Cells(OMRw, 1), Cells(OMRw, 3)).VerticalAlignment = xlCenter
                    Range(Cells(OMRw, 1), Cells(OMRw, 3)).MergeCells = True
                    .Range("A2:C2").Copy Cells(OMRw + 1, 1) ' Section headings
                    OMRw = OMRw + 2
    
                    endrw = .Range("A" & .Rows.Count).End(xlUp).Row
                    For rw = 3 To endrw
                        If .Cells(rw, 5).Value <> "" Then ' Selected part
                            .Range(.Cells(rw, 1), .Cells(rw, 3)).Copy Cells(OMRw, 1)
                            OMRw = OMRw + 1
                        End If
                    Next
                    OMRw = OMRw + 1
                End If
            End If
        End With
    Next
End Sub