Pull Db health status check framework outside BBM namespace

What does this MR do and why?

As the first step to achieve #404898 (closed), this MR pulls the existing database health status check library out of 'lib/gitlab/database/background_migration' folder and places in 'lib/gitlab/database'.

Also alters the HealthStatus.evaluate method to receive 'context' from any callers instead of just batched_migrations.

Note: Started with MR#119187 which has the entire changeset and became huge so splitting it into smaller MRs to have more control.

Screenshots or screen recordings

N/A since it's only structural changes.

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 #404898 (closed)