Ensure to use configured timeouts in http.Server

What does this MR do?

Ensure to use configured timeouts in http.Server

Related to: https://gitlab.com/gitlab-org/gitlab-pages/-/issues/1064

TODO

• Feature flag
  • Added feature flag:
  • This feature does not require a feature flag
• I added the Changelog trailer to the commits that need to be included in the changelog (e.g. Changelog: added)
• I added unit tests or they are not required
• I added acceptance tests or they are not required
• I added documentation (or it's not required)
• I followed code review guidelines
• I followed Go Style guidelines