How to save Tab stops created on a TextEdit document on a MacBook Pro wIth macOS Mojave?

You save the TextEdit document as a rich text (RTF) document. Even so, your indented tab stop will not appear on the reopened RTF document's ruler until you click in front of the text that you have indented. Then the indent mark will appear on the ruler. So for all intents and purposes, you cannot actually save the indent marks in TextEdit and have them automatically appear on the ruler without the prior ritual.

Some may perceive TextEdit as a word processing application, but I do not. If you want to create indents, and actually see them on the ruler upon saving and reopening the document, then use the free Pages application, or any other real word processing application.