Edit issues and Schedule issues are correct.

Schedule issues grants the ability to change scheduling fields and to move and reorder issues on the backlog and board so this permission is required to reorder backlog items on the Scrum board.

Edit issues allows a user to modify issue fields and details which is often required when repositioning or updating work items because reordering can involve changing sprint or ranking fields and the user needs edit rights to persist those changes.

Manage sprints is focused on creating, starting, and closing sprints and it alone does not allow reordering backlog items if the user lacks scheduling or edit rights.

Administer projects is a high level permission for changing project settings and roles and it is not required just to reorder backlog items and it is usually overprivileged for this task.

View development tools only controls visibility of development information such as commits and pull requests and it does not grant the ability to change backlog order.

Browse projects only allows viewing project issues and does not include rights to edit or schedule issues so it cannot be used to reorder the backlog.

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