As soon as the issue is assigned to a request type the Assignee list should load from a specific set of users instead of loading all users in the cloud.
The list of possible assignees is determined only by the "can be assigned issues" permission in your project permissions.
You can easily cut that from "all users" to "only people in a certain role in the project" (or other similar rules), but it's not done by request or issue type, it's all about the user's roles.
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