OnionShare supports four modes: share (one-time file send), receive (others upload to you), website (static .onion site), and chat (anonymous group chat). All four can run persistently on a VPS. The VPS install uses the same onionshare-cli binary that the desktop app uses, just in headless persistent mode without the GUI wrapper.
Persistent mode stores the v3 onion key in a JSON file so the .onion address survives daemon restarts. Without persistence, every restart generates a new address and every existing user loses their bookmark.