[Feature flag] Remove `use_typhoeus_elasticsearch_adapter` flag

Summary

This issue is to remove the feature from production. The flag was never enabled and we have chosen to remove it.

All code that references the use_typhoeus_elasticsearch_adapter feature flag should be removed following the removal process.

Owners

• Team: groupglobal search
• Most appropriate slack channel to reach out to: #g_global_search
• Best individual to reach out to: @john-mason
• PM: @JohnMcGuire