Remove using 3rd party gems

[emmahsax]

Changes

Remove the use of 3rd party gems to do API work, such as the Gitlab gem and the Octokit gem. Although it means that there's a bit more code for me to maintain myself, it ends up being more to my benefit. Here's the motivation for this:

1. The Gitlab gem doesn't really seem to be maintained by the owner, meaning it only gets updates when other people submit pull requests and they're accepted. But, even with that, there's not very many new releases created. I've also seen several places where the gem is using a deprecated version of the GitLab API, which makes me nervous since it doesn't receive updates frequently.
2. The Octokit gem has a bunch of other dependencies, such as Faraday. And the more gems this project requires, the more gems there are to update regularly. Which means that we're further at the mercy of other gems' bugs and warning deprecations (see the note in Update requirements on gems #65). By removing the Octokit gem, we're no longer seeing the issues with those.

Because there are a lot of changes in this merge request, and they may not all be found in my current testing, I'm going to leave this pull request open for a while. I'm going to build the test gem locally on all of my machines, and use them in my daily coding life for a minimum of two weeks to see if any other bugs pop up that need to be addressed. By the time this is released formally, it should have no changing functionality for users, so it's essentially just a big refactor.

Related Pull Requests and Issues

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Additional Context

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[emmahsax]

At this point, this pull request has been tested on all projects I use regularly, both on GitLab and GitHub. I believe this is good to be merged and released as a new minor version.