Remove `gitlab_employee_badge` feature flag

What does this MR do and why?

Related to #410312 (closed)

In &3241 (closed) we started a feature that added a badge for GitLab team members. We never finished the feature because there were higher priorities and there were concerns that it didn't provide value to our self-managed customers.

Recently we introduced &9429 which is a more flexible way to indicate a user is a GitLab team member. This feature will replace the code behind the gitlab_employee_badge feature flag so we are removing the code.

Screenshots or screen recordings

No visual changes, gitlab_employee_badge feature flag was never enabled.

How to set up and validate locally

No visual changes, gitlab_employee_badge feature flag was never enabled.

MR acceptance checklist

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

• I have evaluated the MR acceptance checklist for this MR.