might be the permission issue? (because user will not in the list if he/she do not have permission to work on ticket.
I have given the user the administrator role. Still I don’t see him in the assignee list when I want to assign a task to the other user after adding a comment or changing the task status.
Check your permission scheme, look who has the assignable user permission.
Admin does not mean "can do everything", it means "can do admin tasks" (admin can do everything is a dreadful approach and Atlassian don't do it). You need to add them to a role that has the assignable user permission, as Udo says.
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