Refactor APIBaseTask

[bjtitus]

APIBaseTask has three separate methods for GET, POST, and DELETE request and response handling.

Since much of this code is duplicated and the rest is evident from the parameters, these should be unified so we have a single implementation to ensure they don't diverge.

Additionally, the class should be tested for a few things like error handling specific to DELETE and POST requests and custom header additions.

See this branch for more details.

### Tasks