decouple integration tests from depending on the `Server` header

It is a common practice to override / remove headers added by API Gateway - we should not depend on them in our tests / code.
Our CI needs to be updated to not depend on `Server` header used for AI Gateway instance identification.

Start by searching the integration tests and CI configuration for dependencies on the `Server` header and its AI Gateway instance-identification use. Update those checks so they do not rely on that header, then run the affected integration tests and CI workflow to confirm they pass when the header is overridden or removed.

Written by the indexing model from the issue text.