[Enhancement] Convert lib/model/dav.js into a proper lib/model/dav.ts file

The file was copied from something that works but is very much hard to maintain as it is.

Because the functionality needed from it is quite limited, it's possible to implement it as a standalone class (following the other examples in `lib/models`) which makes simple and predictable XML requests and parses the responses, without needing any extra dependencies.

It'll also have the advantage of being faster, by not having to make unnecessary HTTP calls, which I think can happen right now.