Progress bar

First move the routine out of the user form to a standard code module.

Then remove the demonstration loop I used and place progress update within your existing loops.

'THIS SUB RUNS THE "RUN PROGRESS METER" BUTTON
Sub copyEquals()

' Progress Bar
    Dim frmProgress As UserForm1
    Dim lngIndex As Long
    Dim sngPercent As Single
    Dim lngMax As Long
    
    Dim Sht1Rng As Range, Sht2Rng As Range
    Dim Sht1Rng1 As Range, Sht2Rng1 As Range
    Dim OuterCell As Range, InnerCell As Range, Cell As Range, OuterCell2 As Range
    
    Set frmProgress = New UserForm1
    
    Set Sht1Rng = Range("Sht1") 'Named range for small table
    Set Sht1Rng1 = Range("Sht11") 'Named range for long table
    Set Sht2Rng = Range("Sht2") 'Named range for xfer of small table data
    Set Sht2Rng1 = Range("Sht21") 'Named range for xfer of long table data
        
    Application.Cursor = xlWait
    lngMax = Sht2Rng.Resize(, 1).Cells.Count + Sht2Rng1.Resize(, 1).Cells.Count
    sngPercent = lngIndex / lngMax
    frmProgress.ProgressStyle1 sngPercent, True
    frmProgress.Show vbModeless
    
    '------------------------
    ' Your code would go here
    
    For Each OuterCell In Sht2Rng.Resize(, 1)
        For Each InnerCell In Sht1Rng.Resize(, 1)
            'If OuterCell.Value = InnerCell.Value Then
            If InStr(1, OuterCell.Value, InnerCell.Value) Then
                OuterCell.Offset(0, 1).Value = OuterCell.Offset(0, 1).Value + InnerCell.Offset(0, 1).Value
            End If
        Next
        lngIndex = lngIndex + 1
        sngPercent = lngIndex / lngMax
        frmProgress.ProgressStyle1 sngPercent, True
        DoEvents
    Next
    
    For Each OuterCell2 In Sht2Rng1.Resize(, 1)
        For Each Cell In Sht1Rng1.Resize(, 1)
            'If Right(OuterCell2.Value, ((Len(OuterCell2.Value) - 2) - _
            InStr(OuterCell2.Value, "By"))) = Cell.Value Then
            If InStr(1, OuterCell2.Value, Cell) Then
                'MsgBox "OuterCell2.Value " & OuterCell2.Value
                'MsgBox "Cell value " & cell.Value
                OuterCell2.Offset(0, 1).Value = OuterCell2.Offset(0, 1).Value + Cell.Offset(0, 1).Value
            End If
        Next
        lngIndex = lngIndex + 1
        sngPercent = lngIndex / lngMax
        frmProgress.ProgressStyle1 sngPercent, True
        DoEvents
    Next
    
        
    Application.Cursor = xlDefault
    Unload frmProgress
    
End Sub

Yes as long as you include all the relevant controls.

But if you change you code so it only works with the data rather than the +100k cells in D:E then a progress bar is redundent

    Set Sht1Rng1 = Intersect(ActiveSheet.UsedRange, Range("Sht11")) 'Named range for long table