Convert all of `server/` to TypeScript

[keggsmurph21]

Now everything is written in TypeScript! We can actually start cleaning up the code a little bit now...

The other good news is that notatrix no longer requires a separate "build" step, since the client/ and server/ project can just "consume" it directly.

This PR also includes a bit of reorganization: where before we had

.
├── client
│   └── ...
├── notatrix
│   └── src
│       └── ...
└── servers
    └── ...

we now have

.
└── src
    ├── client
    │   └── ...
    ├── notatrix
    │   └── ...
    └── servers
        └── ...

[keggsmurph21]

fyi @jonorthwash @zensho