When you press Alt+F7 in Total Commander, you have access to really powerful search functionality. Unfortunately, the
Load/Save tab allows loading and saving of search parameters, not the search results.
However, there's a hidden gem that allows you to copy search results to clipboard and then you can paste them to Notepad and save them to file. Just press Ctrl+C when list of search results is focused. A single "blink" of window will tell you that contents are copied to clipboard.