Implement ConnectAPI client in typescript

[zackverham]

Fixed by: #3673

[nealrichardson]

I can't believe I'm suggesting this but: does this help? https://github.com/rstudio/rsconnect-ts could/should we make it useful? I did update it to be using v1 APIs recently.

[zackverham]

woah - I didn't even know that existed. I'm not sure if introducing that as an external dependency is actually better or worse than what I have currently: #3673