[EEM] Migrate API integration tests to the deployment agnostic solution

[maryam-saeidi]

🍒 Summary

We need to migrate API integration tests to the deployment-agnostic solution to ensure they can be run on the serverless environment and avoid duplication.
https://github.com/elastic/kibana/blob/main/x-pack/test/api_integration/deployment_agnostic/README.md

Important

Please make sure to run these tests on MKI before merging the related PR. (More info)

Existing tests

Test	ESS	Serverless	Notes
Built-in definitions	✅	❌	Serverless: N/A ESS: x-pack/test/api_integration/apis/entity_manager/builtin_definitions.ts
Custom definitions	✅	❌	Serverless: N/A ESS: x-pack/test/api_integration/apis/entity_manager/definitions.ts

[elasticmachine]

Pinging @elastic/obs-knowledge-team (Team:obs-knowledge)

[elasticmachine]

Pinging @elastic/obs-entities (Team:obs-entities)