Migrate `epics_deepest_relationship_level` to instrumentation class

What does this MR do and why?

Recently it was discovered #374591 (closed), that epics_deepest_relationship_level Service Ping metric does not implement proper error handling and caused outgate of whole Service Ping reporting process. This commit move epics_deepest_relationship_level metric to new instrumentation classes framework that assures secured isolated metric execution

Screenshots or screen recordings

Screenshots are required for UI changes, and strongly recommended for all other merge requests.

How to set up and validate locally

payload = ServicePing::BuildPayload.new.execute
 payload["counts"]["epics_deepest_relationship_level"]

Numbered steps to set up and validate the change are strongly suggested.

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 #374601 (closed)