Typescriptify the `sync/` endpoint and `Sync.ts`

[ibeckermayer]

See https://github.com/vector-im/hydrogen-web/commit/295edfc7fcab9cedce0d9e6783feba7b328792ea for what amounts to a proposed direction for typing Matrix API responses.

The rest of the changes type Sync.js --> Sync.ts plus any incidental changes required in that process.