Adjust the test model health check

What does this MR do and why?

Related to #517097 (comment 2368206532) and #521653 (closed)

Summary:

The service at ee/lib/gitlab/llm/ai_gateway/code_suggestions_client.rb is testing code suggestions. However, in self-hosted environments, the test should be performed using self_hosted_models.

Changes in this MR:

• Adjusted the test model health check.
• Ensured the correct service_name is used for self-hosted environments when self-hosted models are available.

Verification:

Recording (Internal, as the recording reveals a machine IP).