[Detections Response] Finish moving remaining legacy FTRs (#175837)

**Resolves: #151902

## Summary

After this PR, all D&R FTRs are moved to new folder where they can be
run in ESS and serverless. Please see below table for a summary of what
tests need revisiting by the teams. During the test migration there may
have been some tests that failed on serverless, but not ESS. Some we
were able to fix and get running on both, others are still marked as
`brokenInServerless` and need triage.

.buildkite/ftr_configs.yml

@@ -6,7 +6,6 @@ disabled:
   - test/functional/config.base.js
   - test/functional/firefox/config.base.ts
   - x-pack/test/functional/config.base.js
-  - x-pack/test/detection_engine_api_integration/security_and_spaces/config.base.ts
   - x-pack/test/functional_enterprise_search/base_config.ts
   - x-pack/test/localization/config.base.ts
   - test/server_integration/config.base.js
@@ -232,7 +231,6 @@ enabled:
   - x-pack/test/cloud_security_posture_functional/config.ts
   - x-pack/test/cloud_security_posture_api/config.ts
   - x-pack/test/dataset_quality_api_integration/basic/config.ts
-  - x-pack/test/detection_engine_api_integration/basic/config.ts
   - x-pack/test/disable_ems/config.ts
   - x-pack/test/encrypted_saved_objects_api_integration/config.ts
   - x-pack/test/examples/config.ts
@@ -493,8 +491,12 @@ enabled:
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_creation/trial_license_complete_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_patch/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_patch/trial_license_complete_tier/configs/serverless.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_patch/basic_license_essentials_tier/configs/ess.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_patch/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_update/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_update/trial_license_complete_tier/configs/serverless.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_update/basic_license_essentials_tier/configs/ess.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_update/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/prebuilt_rules/bundled_prebuilt_rules_package/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/prebuilt_rules/bundled_prebuilt_rules_package/trial_license_complete_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/prebuilt_rules/large_prebuilt_rules_package/trial_license_complete_tier/configs/ess.config.ts
@@ -507,14 +509,20 @@ enabled:
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_bulk_actions/trial_license_complete_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_delete/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_delete/trial_license_complete_tier/configs/serverless.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_delete/basic_license_essentials_tier/configs/ess.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_delete/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_import_export/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_import_export/trial_license_complete_tier/configs/serverless.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_import_export/basic_license_essentials_tier/configs/ess.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_import_export/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_management/basic_license_essentials_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_management/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_management/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_management/trial_license_complete_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_read/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_read/trial_license_complete_tier/configs/serverless.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_read/basic_license_essentials_tier/configs/ess.config.ts
+  - x-pack/test/security_solution_api_integration/test_suites/detections_response/rules_management/rule_read/basic_license_essentials_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/telemetry/trial_license_complete_tier/configs/ess.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/telemetry/trial_license_complete_tier/configs/serverless.config.ts
   - x-pack/test/security_solution_api_integration/test_suites/detections_response/user_roles/trial_license_complete_tier/configs/ess.config.ts