I have a post function that will create a subtask. I would like to use the value of a scripted field in the summary of the subtask.
I can confirm that currently that it is not possible to search in JQL for the values of Scripted Fields provided by ScriptRunner for Jira Cloud as this currently not a feature that we provide.
We can, however, confirm that we do have this on our roadmap as a feature request here and I would ask you to vote on this if this something that you are interested in so that our development team can see this and consider this as a feature to be added in future.
Also, I can confirm that Scripted Fields are calculated when an issue is loaded in Jira cloud and are a special field type rather than a standard custom field type like in Jira server.
The reason for this is due to the API's that Atlassian provided being different between Jira Server and Jira Cloud.
This means that Scripted Fields are only designed to be viewed on issues and cannot be used inside of other scripts.
If you need to use these values inside of other scripts then you will need to use a Script Listener to calculate the value into a standard custom field on an Issue Updated event similar to the example we have here as this will then allow the value to be saved inside a standard custom field that can be used in other scripts.