https://docs.github.com/en/rest/using-the-rest-api/rate-limits-for-the-rest-api?apiVersion=2022-11-28#exceeding-the-rate-limit

If you exceed your primary rate limit, you will receive a 403 or 429 response, and the x-ratelimit-remaining header will be 0. You should not retry your request until after the time specified by the x-ratelimit-reset header.

If you exceed a secondary rate limit, you will receive a 403 or 429 response and an error message that indicates that you exceeded a secondary rate limit. If the retry-after response header is present, you should not retry your request until after that many seconds has elapsed. If the x-ratelimit-remaining header is 0, you should not retry your request until after the time, in UTC epoch seconds, specified by the x-ratelimit-reset header. Otherwise, wait for at least one minute before retrying. If your request continues to fail due to a secondary rate limit, wait for an exponentially increasing amount of time between retries, and throw an error after a specific number of retries.

Continuing to make requests while you are rate limited may result in the banning of your integration.

I think GitHub.jl's request code should implement the retry logic outlined above. This is a bit annoying as HTTP.jl doesn't allow that much flexibility (JuliaWeb/HTTP.jl#1234) but we can do the retries manually.