Refactor `proxy` module into TS

[jescalada]

Is your feature request related to a problem? Please describe.
As part of the #276 epic, we could split the TS refactor down into more manageable chunks:

• Frontend
• Backend
  • service: Web service/auth layer
  • proxy: Proxy logic
  • Auxiliary modules
    • config
    • db
• Tests

Describe the solution you'd like
This issue is only for the proxy module (actions, processors, routes).

Describe alternatives you've considered
None.

Additional context
#927