Resolve "Convert the schema validation framework into a gem"

What does this MR do and why?

In the previous merge requests (!125597 (merged) and !124727 (merged)), we created a new gem where we added the logic of the schema-validation framework.

In this merge request, we remove the schema-validation files from the GitLab codebase and switch the app to use the gem.

How to set up and validate locally

Run the following rake task: bundle exec rake gitlab:db:schema_checker:run

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.

Related to #390856 (closed)