Jira API endpoint to update select (single multi or cascading) for contexts

Hi there.
Is it possible via the API to update select (single multi or cascading) options for specific contexts? Not ust the global context configuration?

In addition to the above, is it possible to have contexts within a Project (Service Desk) - ie. have a bunch of options in a dropdown only display based on certain conditions or field values?

Please let me know if you require more clarification?
Thank you

Any feedback or updates on this please? Thank you