Add Logging to AiGateway Component

What does this MR do and why?

Relates to https://gitlab.com/gitlab-org/quality/quality-engineering/team-tasks/-/issues/2277

This MR enables logging on the AI Gateway component and makes the logs available in job artifacts to more easily troubleshoot AI gateway errors during test failures.

An example artifact of the modelgateway_debug.log can be found here: https://gitlab.com/gitlab-org/gitlab-qa/-/jobs/6522166598/artifacts/browse/gitlab-qa-run-2024-04-01-17-48-28-e2906d82/ai-gateway/logs/

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• Commits include Changelog: trailer
• I have evaluated the MR acceptance checklist for this MR.