For stateless applications it is pretty obvious how supervision trees can improve the reliability. Essentially the only ‘state’ there is request itself. Worst case scenario client would just retry.
But with some state involved it becomes not as simple.
Essentially the answer to my question probably would be like : “you should store the state in the external system, and design your system in such a way that stored state is always consistent. In case of failure supervisor will respawn the process and it will recreate what it needs from the saved state”