are there any appliances that can automate feeding of sourdough starter?
I have not heard of any machine of that nature, and I try to keep up with an assortment of home beer brewing sources.  If anyone would have come up with something, it would probably be brewers, since we tend to use large amounts of live yeast.    About the most advanced thing I have heard of is storing wort in Nalgene bottles after boiling and using that for a starter.   I can't think of an analog for sourdough that would be safe and keep the starter maintained with a good flavor.   Pro brewers or bakers may have a tool that I'm unaware of, though.

I'm sure you could come up with some sort of Rube Goldberg machine to feed your starter, but really, it's like taking care of any living thing.   You have to water and feed plants, animals, and yeast cultures.   It's a small amount of work, too, really.   Add water, flour, maybe some sugar, and stir.   You might want to stick with non-sourdough breads if you can't make that kind of time investment.