Cleaning up the GitHub auth

The GitHub auth code has been refactored in a major effort which started with fixing #1118 and #1119 in #1205, and continued in #1736, #1812, #1813, #1861, #1862, #1906, #1939, #2021, #2253, and #2400. The last of that is finally merged. 😌

There were a couple bugs in that which are being patched in #2730 though there's some outstanding work that would leave this in a cleaner shape. I wanted to capture it here and hash out what ought to be done, then maybe open issues for the smaller pieces.

1. It should be possible to configure more than one static token, for self-hosting. Maybe this would involve changing `GITHUB_TOKEN` to `GITHUB_TOKENS`.
2. Dynamic tokens should be configurable. When that's turned off, token persistence and the token endpoint should be turned off.
3. However _the pool itself_ could be used all the time; there's not a big advantage in turning that off when it doesn't need to be used.
4. We should make sure it's possible to run GitHub badges without a token, up to the unauthenticated limit. (#2754)

Start by reviewing the completed authentication work referenced in #1205, #1736, #1812, #1813, #1861, #1862, #1906, #1939, #2021, #2253, and #2400, along with the bugs in #2730. Resolve the four configuration and unauthenticated-badge questions, including the relationship to #2754; the issue does not name files or tests.

Written by the indexing model from the issue text.