Display Full Text within Textbox (On A UserForm) when you hover over the textbox

You could put this in the Userform code module

Private Sub TextBox1_Change()
    TextBox1.ControlTipText = TextBox1.Text
End Sub

No, I don't know how to wrap the control tip. Even inserting a vbCrLf doesn't make it more than one line.

I might try a Lable whose visibility is controlled by the TextBox's MouseMove event.
Create a Class module named clsHoverLabel with this code in it.

' in clsHoverLabel

Public WithEvents myTextBox As MSForms.TextBox
Public WithEvents myLabel As MSForms.Label
Dim ShowMe As Boolean

Private Function CreateLabel() As MSForms.Label
    Set CreateLabel = myTextBox.Parent.Controls.Add("forms.Label.1")
    With CreateLabel
        .AutoSize = False
        .BackColor = vbYellow
        .BackStyle = fmBackStyleOpaque
        .BorderStyle = fmBorderStyleSingle
        .Width = myTextBox.Width
        .Visible = False
        .Caption = myTextBox.Text
        .AutoSize = True
        .Top = myTextBox.Top + myTextBox.Height + 5
        .Left = myTextBox.Left + 10
    End With
    Set myLabel = CreateLabel
End Function

Property Set TextBox(inBox As MSForms.TextBox)
    Set myTextBox = inBox
    CreateLabel
End Property

Property Get Visible() As Boolean
    Visible = myLabel.Visible
End Property
Property Let Visible(inVal As Boolean)
    myLabel.Visible = inVal And (Len(myTextBox.Text) > 0)
End Property

Private Sub myLabel_Click()
    myLabel.Visible = False
End Sub

Private Sub myTextBox_Change()
    With myLabel
        .AutoSize = False
        .Caption = myTextBox.Text
        .Width = myTextBox.Width * 2
        .AutoSize = True
        .AutoSize = False
        .Width = WorksheetFunction.Max(.Width, myTextBox.Width)
        .Visible = (Len(myTextBox.Text) > 0) And Me.Visible
    End With
End Sub

Private Sub myTextBox_MouseMove(ByVal Button As Integer, ByVal Shift As Integer, ByVal X As Single, ByVal Y As Single)
    With myTextBox
        If X < 2 Or Y < 2 Or (.Width - X) < 2 Or (.Height - Y) < 2 Then
            Me.Visible = False
        Else
            Me.Visible = True
        End If
    End With
End Sub

Then put code like this in the userform's code module

Dim LabeledTextbox As clsHoverLabel

Private Sub UserForm_Initialize()
    Set LabeledTextbox = New clsHoverLabel
    Set LabeledTextbox.TextBox = TextBox1
End Sub