Improve Code Quality of the Study Manager Endpoint

We will raise the overall code quality of the Study Manager endpoint through a structured, multi-step process. The goal is a cleaner architecture, clearer responsibilities, and a stable contract between backend and frontend:

## 1. Gather UI Requirements
- **Goal:** Understand exactly what the UI needs from the backend.
- **Tasks:**
- [ ] #90
- [ ] #91
- [ ] #92
- [ ] #93

## 2. Implement Backend Improvements
- **Goal:** Refactor or implement backend logic based on the architecture plan.
- **Tasks:**
- [ ] #95

## 3. Adjust Frontend if Contract Changes
- **Goal:** Align the frontend with any refined backend behavior.
- **Tasks:**
- [ ] Update frontend API calls and data models if endpoint details changed
- Refer to #91 and #92
- [ ] Verify the UI flows against the new backend behavior (manual testing)