Anecdotally, the v2 api appears to treat project slug in a case-sensitive manner. This very well may be side effect of its placement in the path of the URI (https://tools.ietf.org/html/draft-ietf-httpbis-p1-messaging-25#section-2.7.3) for the API resources I've tested against.
Regardless, I'm unable to find a clear statement in the v2 docs whether or not slug is case-sensitive.
https://discuss.circleci.com/t/github-case-insensitive-org-name/23899 hints that this has been a source of confusion for a while.