Series content is the worst thing to lose mid-watch because tracking where you left off in someone else's uploads is a genuine mess. Downloading as you go means you always have them in the right order whenever you want to continue.
Online TikTok Downloader is the right tool for this, files come out clean and you can rename and sort them as you go rather than juggling bookmarks across a long multi-part run. Did this with a cooking series that ran nearly twenty parts and having them all in a numbered folder made such a difference. Watched the whole thing on a flight without touching the app once