[ResponseOps] Switch from the deprecated Security APIs to the Core APIs

[cnasikas]

The security plugin is now a first-class citizen of the Kibana Core. The following platform security APIs are now accessible via Core services and the Core's request handler context:

• authentication: core.security.authc
• user profile: core.userProfile
• audit logging: core.security.auditLogging

We should change our plugins to use the Core APIs instead of the deprecated Security APIs.

Plugins

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1. actions [Actions Plugin] Use server-side authc.getCurrentUser from core.security #186924
2. alerting [Alerting Plugin] Migrate authc.getCurrentUser usage to core.security #187020
3. cases Migrate authc dependency from security plugin to core security service #187124
4. triggers_actions_ui
5. stack_connectors
6. stack_alerts
7. task_manager
8. event_log
9. rule_registry
10. examples/alerting_example
11. examples/triggers_actions_ui_example
12. examples/gen_ai_streaming_response_example
13. cases_api_integration/common/plugins
14. alerting_api_integration/common/plugins
15. functional_with_es_ssl/plugins
16. test/plugin_api_integration/plugins
17. test/plugin_api_perf/plugins/task_manager_performance

Related issue: #174578

[elasticmachine]

Pinging @elastic/response-ops (Team:ResponseOps)