When I set up a local wiki with CentralAuth and CheckUser enabled, and $wgCheckUserLogLogins = true, and a crude approximation of the shared authentication domain, I get
POST https://login.wiki.local.wmftest.net:11048/w/rest.php/checkuser/v0/useragent-clienthints/privatelog/57 500 (Internal Server Error)
This is expected inasmuch as we are intentionally disabling non-authentication-related APIs on the shared domain, but this is sort of authentication related. We should either enable it (that would require adding a new hook to the REST API), or stop CheckUser from making this request (by overriding mw.config.get( 'wgCheckUserClientHintsPrivateEventId' )).