Refactor of the with*HttpPubApiClient method(s).

[isoos]

• follow-up to Refactor proposal: use unnamed callback function in with*HttpPubApiClient methods. #8490
• the Http part of the method name is not that relevant (since IIRC we no longer have the non-HTTP version)
• replacing it with Retry to follow the pattern of other similar helper methods
• renamed bearerToken -> authToken as the bearer part is only a technical detail
• renamed experimental -> experiments as we pass on the list of experiments and not the experimental cookie value