[Ingest Manager] Migrate all API integration tests to use dockerized registry

[jen-huang]

Now that we have an API integration test folder setup that uses a dockerized registry (#69822), we should move our other tests to this folder so that they use the docker service: https://github.com/elastic/kibana/tree/master/x-pack/test/ingest_manager_api_integration

This will let us avoid test failures related to unreachable registry URL, such as: #68568 (comment).

A non-exhaustive list of the test needing migration:
https://github.com/elastic/kibana/tree/master/x-pack/test/api_integration/apis/fleet
https://github.com/elastic/kibana/tree/master/x-pack/test/api_integration/apis/ingest_manager

There is also a defunct integration test folder within the plugin directory that should assessed and removed/migrated:
https://github.com/elastic/kibana/tree/master/x-pack/plugins/ingest_manager/server/integration_tests

Bonus: add more coverage as part of this migration effort!!

[elasticmachine]

Pinging @elastic/ingest-management (Team:Ingest Management)