Would it be within the scope of this project to add an autosave feature (either upon each edit or on a relatively short interval)? I would like to write an OBS plugin or small program that can render tmx maps with an embedded tileset, with the use case being using tiled's infinite map mode as a live "dungeon crawler" mapper for old DOS or console games for those that do not want to or cannot use an automapper. This would allow a streamer to show their mapping progress on stream when desired without manually having to save after each edit.
I think an autosave feature would be nice to have in general, but I also really like your idea of using Tiled as a tool to keep track of the explored area and to stream that using OBS. Instead of a plugin, possibly the "tmxviewer" application could be used to render the map, if only it would automatically reload the map file on changes (which is something that could be implemented). Of course a plugin could add functionality that would not be possible with an external application.
I've opened an issue about an autosave feature.