Use GitLab Logger to handle GitLab Shell logs

What does this MR do?

Use containerized GitLab Logger instead of xtail to handle the log files

Related issues

Closes: gitlab-org/charts/gitlab#2429 (closed)

Checklist

See Definition of done.

For anything in this list which will not be completed, please provide a reason in the MR discussion

Required

• Merge Request Title, and Description are up to date, accurate, and descriptive
• MR targeting the appropriate branch
• MR has a green pipeline on GitLab.com

Expected (please provide an explanation if not completing)

• Test plan indicating conditions for success has been posted and passes
• Documentation created/updated
• Integration tests added to GitLab QA
• The impact any change in container size has should be evaluated