Tab Shelf reads the export files of the most common tab managers and recognises the format by its content, so you don't have to tell it what the file is. Nothing is uploaded: the file is read inside your browser.
Open Toby → Settings (gear icon) → Export. You get a .json file with all your lists. Each list becomes a Tab Shelf session.
Workona → Settings → Export your data. Each workspace becomes a session; its sections become tab groups.
OneTab → Export / Import URLs → copy the text into a .txt file. Each block of links becomes a session.
Session Buddy → session → Export → JSON. Windows and pinned tabs are preserved.
Bookmark manager → Export bookmarks (an .html file). Each folder becomes a session.
A plain text file with one URL per line works too, and so does most JSON that contains links.
Click the Tab Shelf icon → Open manager → Import… → choose the file. A message tells you how many sessions were created. Existing sessions are kept; nothing is overwritten.
Open a couple of imported sessions and restore one in a new window. When you're happy, you can remove the old extension — or keep it: Tab Shelf doesn't interfere with other tab managers.