Out of the box on Jira you can't do this thing. Your best case is to use scriptrunner and develop a script. E.g. scriptrunner provides a built-in post function which you can take and make it work as a "Behavior" https://docs.adaptavist.com/sr4js/latest/features/workflows/post-functions/built-in-post-functions/assign-to-first-member-of-role
And just to be clear, since you want people to be able to assign to a specific group of people, then you want to try to control it via a behavior and not a post function.
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