By supporting WebDav your app will instantly gain the possibility to sync with every OS and a gazillion apps. It is not the best protocol, but it's everywhere and it's very good when implemented well. For example, CopyParty's WebDav implementation is blazing fast.
Afterwards, you could enhance the experience by supporting websockets so that contributors can build clients specific to your project. This will take much more time to reach the user with a usable sync app, but can potentially end up in a superior experience.
Imagine a Google Pixel level phone made by Valve, running Steam OS (Linux) on ARM. That's my nerd wet dream.