If you didn't backup the bookmarks and no other system is sync and this is the sole computer then the chances to recover won't find the sync data. And if you reinstalled the System the new Firefox probably cleared any prior sync data since the new Firefox install has nothing to sync it will sync with that version and if no data then the data will be cleared to match current Firefox data that would be the default but not data you created. If you had used Firefox bookmark save FAQ then you would have the bookmark saved on a USB device to restore them back but as you mentioned they aren't locally saved which would me there nothing to restore back to Firefox. And with a system OS reinstall that usually wipes clean any data if that is the same computer will had no recover data to be found as OS install makes a fresh install wiping everything clean to start as well.