Hello monhw,

This version of your macro should do the job. Since the macro is being run from an Excel workbook, there is no reason to create a separate instance of Excel. You can open the other workbook in the current instance.
Sub GetData1()

    Dim Data As Range
    Dim DstRng As Range
    Dim ID As Variant
    Dim SrcRng As Range
    Dim SrcWkb As Workbook
    
        Set SrcWkb = Excel.Workbooks.Open("C:\Users\e156476\Documents\Data\System Queries\ExcelForm_data.xlsm")
        Set SrcRng = SrcWkb.Worksheets("Data").Range("A1").CurrentRegion
        
        Set DstRng = ThisWorkbook.Worksheets("Result").Range("B3:B9")
        ID = ThisWorkbook.Worksheets("Result").Range("B1").Value
        
        Set Data = SrcRng.Columns(1).Cells.Find(ID, , xlValues, xlWhole, xlByRows, xlNext, False)
        
        If Not Data Is Nothing Then
            DstRng.Value = Application.Transpose(Data.Resize(1, 7))
        End If
        
End Sub