Counting the matching substrings in range

See if the code below helps you:

Public Sub TestCount()
    lastrow = Range("Q" & Rows.Count).End(xlUp).Row
    strformula = "=SUMPRODUCT(LEN(Q1:Q" & lastrow & ")-LEN(SUBSTITUTE(UPPER(Q1:Q" & lastrow & "),""/ST"","""")))/LEN(""/St"")"
    MsgBox Evaluate(strformula)
End Sub

I think you can count the number of characters, replace your "St/" with nothing and then count the characters again and divide by len("St/"). Here's an example.

'''your existing code
Dim lCount As Long
Dim lCount_After As Long
'''set a Range to column Q
Set oRng = Range("Q1:Q" & lRow_last)
'''turn that range into a string
sValues = CStr(Join(Application.Transpose(oRng.Value2)))
lCount = Len(sValues)
lCount_After = lCount - Len(Replace(sValues, "St/", ""))
lCount_After = lCount_After / 3

Debug.Print lCount_After

Using ArrayToText() function

a) If you dispose of Excel version MS365 you can shorten a prior string building by evaluating the tabular ARRAYTOTEXT() formula to get a joined string of all rows at once (complementing @Foxfire 's valid solution).

Note that it's necessary to insert the range address as string; in order to fully qualify the range reference I use an additional External:=True argument.

b) VBA's Split() function eventually allows to return the number of found delimiters (e.g. "St/") via UBound() function. It returns the upper boundary (i.e. the largest available subscript) for this zero-based 1-dimensional split array.

Example: If there exist eight St/ delimiters, the split array consists of nine elements; as it is zero-based the first element has index 0 and the last element gets identified by 8 which is already the wanted function result.

Function CountOccurrencies(rng As Range, Optional delim as String = "St/")
'a) get a final string (avoiding to join cells per row) 
    Dim txt As String
    txt = Evaluate("ArrayToText(" & rng.Address(False, False, External:=True) & ")")
'b) get number of delimiters 
    CountOccurrencies = UBound(Split(txt, delim))
End Function

Not the cleanest one, but you can take all into arrays and split by St/. Size of that array would be how many coincidences you got:

Sub test()
Dim LR As Long
Dim MyText() As String
Dim i As Long
Dim q As Long

LR = Range("Q" & Rows.Count).End(xlUp).Row
ReDim Preserve MyText(1 To LR) As String

For i = 1 To LR Step 1
    MyText(i) = Range("Q" & i).Value
Next i

q = UBound(Split(Join(MyText, ""), "St/"))

Debug.Print q
Erase MyText
End Sub

The output i get is 8

Please, note this code is case sensitive.

The TextJoin() function in Excel 2019+ is used:

Sub CalcSt()
    Const WHAT = "St/": Dim joined As String
    joined = WorksheetFunction.TextJoin("|", True, Columns("Q"))
    Debug.Print (Len(joined) - Len(Replace(joined, WHAT, ""))) / Len(WHAT)
End Sub