If you're referring to the Google Translate widget, then I don't think it provides a callback function to indicate that it has finished translating your web page. The next best thing could be to detect changes in the widget's dropdown selection, and assume that the user has translated the page if the selected item is not the same as what it was before.
Note: Google does not support the Translate widget any more. https://support.google.com/translate/thread/4007370?hl=en
You're going to have to head to Stack Overflow for this. You're going to have to sift through everything that happens in the console when an auto-translator is used, and this is going to vary between browsers. I recommend https://stackoverflow.com/questions/62998768/detecting-auto-translation-event-in-microsoft-edge as a jumping off point.