Consider implementing and hosting backend server / API

FSH Online is currently a client-side only app. It does not require any specific backend server (just a standard HTML server). This allows us to host it on GitHub Pages for free and with minimal maintenance. It also, however, prevents us from being able to implement some advanced features -- and requires _creative_ solutions for things like the _sharing_ feature.

These limitations would go away if we were able to implement and host a backend API -- so it's worth considering. After consideration, we may still decide that the current approach is still the best approach.

Start by reviewing FSH Online’s current client-side architecture, GitHub Pages hosting model, and the sharing feature. Identify which advanced features require a backend API and compare the maintenance and hosting implications with the current approach. Done means documenting a clear decision about whether to implement and host a backend server.

Written by the indexing model from the issue text.