Align two backend modules schema files consistently.

[ianliuwk1019]

Describe the task
The schemas files (schema.py) between two backend modules ("server/backend" and "server/admin_management") are not consistent due to several past historical reasons, even when they might server for the same functionality.
We should make this to be consistent so that developers don't get confused.

Acceptance Criteria

• Naming convention consistent, e.g., DTO or Schema, xyzResponse or xyzRes.
• File separation and grouping the same.
• The impact logic and tests stay the same.
• Api-Client code regenerated.
• Frontend adjustment when needed.

Additional context

• Add any other context about the task here.