Fix E2E test cases and setup for GHA (#26944)

* Fix E2E test cases and setup for GHA
* Fix more test cases, apply recommendations

e2e-tests/.ci/.e2erc

@@ -52,7 +52,7 @@ mme2e_wait_service_healthy () {
   SERVICE_NAME=${1?}
   RETRIES_LEFT=${2:-1}
   RETRIES_INTERVAL=${3:-10}
-  mme2e_wait_command_success "${DC_COMMAND} ps ${SERVICE_NAME} | grep -q '\(healthy\)'" "Waiting for ${SERVICE_NAME} container to be healthy" "$RETRIES_LEFT" "$RETRIES_INTERVAL"
+  mme2e_wait_command_success "${DC_COMMAND} ps ${SERVICE_NAME} | grep -qE '\(healthy\)'" "Waiting for ${SERVICE_NAME} container to be healthy" "$RETRIES_LEFT" "$RETRIES_INTERVAL"
 }
 mme2e_wait_image () {
   IMAGE_NAME=${1?}