async_run_job and async_add_job are deprecated and will be removed in Home Assistant 2025.4. This deprecation does not apply to the sync API add_job method, which is not planned to be removed.
Instead, it's more efficient to use one of the other job methods, as the method of calling the job does not ever have to be worked out:
If the callable is a coroutine function running from a config entry:
entry.async_create_background_task, entry.async_create_task
If the callable is a coroutine function running from another place:
hass.async_create_background_task, hass.async_create_task
If the callable should run in the executor:
hass.async_add_executor_job