Replace custom HTTP mocking setup

[Turbo87]

In the crates.io testsuite we are currently using a custom HTTP mocking setup, based on implementing an HTTP proxy server that intercepts reqwest requests.

This setup is somewhat hard to use though, and it might be possible to use something like https://docs.rs/mockito instead, which could make it easier to understand and write tests for our codebase.

#3121 already introduces the mockito dependency for HTTP mocking of the pagerduty API, but it might be worth investigating if we could use it the same way for the GitHub and S3 API requests.

[Turbo87]

This has been implemented to some degree. Our custom HTTP recorder is a thing of the past now :)