In this scenario I want an automatic change of assignee to our support group user. Is that possible?
Yes it is possible.
You can achieve it with scriptrunner.
You can do it with the script listeners from this plugin. Al tough there are multiple solutions the easiest is probably with the "Fast-track transition an issue"
Set events on "issue commented"
You can leave your condition empty or you can write a condition to check in which group the user is in.
At action you can choose the correct status (make sure you select it from the correct workflow)
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