Right, Tiled is not on Steam for a few reasons. It’s mostly about time and experience. I do not know the process of putting something on Steam, so putting Tiled on Steam will be quite a time investment. Secondly I believe it costs money to put something on Steam. Finally, I want paying for Tiled to be optional, and Steam does not support an optional payment. I’d either have to make it free, in which case it’s hard to justify putting in the time and money for a Steam release, or I’d have to figure out a certain “fair price” and somehow communicate clearly that you can pay anything you want (or even nothing) for Tiled, as long as you get it from somewhere else.
There is precedence also for free software on Steam, like Krita (though it receives bad reviews because it’s an old custom version, you can read more about why here) and Blender (available for free). I would like Tiled to be on there as well, but so far it’s not due to the above problems.
Regarding automatic updates, eventually I hope to add a good built-in solution, but in the meantime I can also recommend you use the itch.io app.