for each sheet with first 3 char matching variable, copy column C to Target sheet unless..

So I've been trying to Copy Column C from Each Sheet that starts with "STU" to Sheet("Target") starting at "A2", there will be other sheets not starting with "STU" but if add additional sheets starting with "STU", I want to enter only the new info to the next blank column stating at row 2.. I'm using the sheet names as the A2 header, then filling in the info under the header, A3.
I've manage to copy the code, use only the sheets i wanted, but it i ran the code a secong time, it just adds all the sheets again, I've tried using application.worksheetfunction.match, tried coping sheet names first, then check cell values against sheets, but am unable to figure it out..

here's the code I've butcher, please don't laugh too hard, I'm trying

Sub Pull_Data()
    'MsgBox "Please Be Patient"
    Dim Cell As Variant
    Dim mRng As Range
    Dim J As Integer
    Dim wsSource As Worksheet
    Dim wsDest As Worksheet
    Dim rng As Range
    Dim drng As Range

    Dim strSourceFile As String
    Dim strSourceDirectory As String
    Dim counter As Long
    Dim i As Long
    
    
    Set wsDest = Sheets("TARGET")
   Count = ThisWorkbook.Worksheets.Count
   
 For Each sh In Sheets
 SName = "STU"
 If Left$(sh.Name, 3) = SName Then
 CName = sh.Name
 Set mRng = Sheets("Target").Range("A2:AA2")
    For Each Cell In mRng
        If Cell.Value = "" Then
        Cell.Value = CName
        GoTo 4
        Else
        
       
       
        With Sheets(CName)
                With Application
                    .ScreenUpdating = False
                    .EnableEvents = False
                End With
                .Activate
                .Select
        Set wsSource = ActiveSheet
        Set drng = wsDest.Range("A3")

                
1
        Do While drng.Value <> ""
          Set drng = drng.Offset(0, 1)
          GoTo 1
          Loop
          drng.Offset(-1, 0).Value = ActiveSheet.Name
            f = 1
2
            Do While ActiveSheet.Range("C" & f).Value = ""
                f = f + 1
                GoTo 2
                Loop
            
                firstrow = Range("C" & f)
                'MsgBox (firstrow.Value)
            
                lastrow = Cells(Rows.Count, "A").End(xlUp).Row
                For i = f To lastrow
                
                    For Each rng In Range("C" & i)
                    drng.Value = rng.Value

                    Next rng
                    Set drng = drng.Offset(1)
               Next i
        End With
3
       

    End If
    Next Cell


 Else

 End If
4
 Next sh

Sheets("Target").Activate
   
End Sub

there's other code, all under workbook, but it doesn't function
and heres the workbook
StuTest V1.xlsm