REST API calls can be used to apply changes on the engine, such as START / STOP / RESTART/ etc.
There is no specific call to output engine status; however, it is still possible the check it by following these steps:
Get the engine ID:
curl --request GET 'https://api.app.firebolt.io/core/v1/account/engines:getIdByName engine_name=YOUR_ENGINE_NAME&account=YOUR_ACCOUNT' --header 'Authorization: Bearer YOUR_ACCESS_TOKEN_VALUE'
Use the retrieved ID in the following call:
curl --request GET 'https://api.app.firebolt.io/core/v1/account/engines/ENGINE_ID' --header 'Authorization: Bearer YOUR_ACCESS_TOKEN_VALUE'
The response will include "current_status_summary" which outputs the current engine status. For example:
"current_status_summary":"ENGINE_STATUS_SUMMARY_STOPPED"
Engine statuses are explained in Firebolt Documentation