Hi there,
I'm unsure what is the purpose to store the session. Even if the session is stored, also keep in mind that the server that serves the request may expire the session at a preset time & due to how process/activity instances can take seconds or days to finish, this may not be practical.
Perhaps you can refer to this answer → https://dev.joget.org/community/display/KBv6/questions/86540330/answers/87097518. It could be helpful to your solution.
And depending on the API you are calling, perhaps you can perform JSON API Authentication so you can retrieve whatever result everytime the api calls.
JSON Tool does not store the session since it creates a new http request every time.