That is correct. Otherwise here is a short macro that you could attach to a keyboard shortcut.
Code:
Sub NormalTemplateSave()
' Charles Kenyon
' 16 March 2022
' Save the Normal Template
Application.ScreenUpdating = False
Application.NormalTemplate.OpenAsDocument
ActiveDocument.Saved = False
ActiveDocument.Close SaveChanges:=True
Application.ScreenUpdating = True
MsgBox "The Normal template has been saved."
Application.ScreenRefresh
End Sub