docs: Add documentation for discovering prompt IDs

Add comprehensive documentation explaining how to discover and use
student and coach prompt IDs when creating conversations.

Content:
- Overview of student and coach prompt systems
- GET /api/personalities endpoint for programmatic discovery
- Complete list of 10 student prompts (grade_1-9, coach_direct)
- Complete list of 3 coach prompts (empathetic, balanced, structured)
- Usage examples for creating conversations
- Notes about defaults and special prompt IDs

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

docs/backend-doc/11-prompt-ids.md

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+# How to Get Prompt IDs
+
+## Summary
+
+Learn how to discover available student and coach prompt IDs for creating conversations. The system provides two types of prompts: student prompts (grade-based personalities) and coach prompts (teaching persona styles).
+
+## Overview
+
+When creating a conversation, you need to specify:
+- **Student Prompt ID**: Determines the student's age, personality, and communication style
+- **Coach Prompt ID**: Determines the coaching style and approach (optional, defaults to "balanced")
+
+## Discovering Student Prompt IDs
+
+### Via API
+
+Use the `/api/personalities` endpoint to programmatically discover available student prompts:
+
+```bash
+curl -X GET http://localhost:3000/api/personalities
+```
+
+**Response:**
+```json
+{
+  "personalities": [
+    {
+      "id": "grade_1",
+      "name": "小一學生 - 7歲",
+      "description": "7歲小一學生，具體思考，句子簡單，尋求認可"
+    },
+    {
+      "id": "grade_2",
+      "name": "小二學生 - 8歲",
+      "description": "8歲小二學生，開始獨立，簡單比較，同儕意識"
+    },
+    ...
+  ],
+  "total": 10
+}
+```
+
+### Available Student Prompt IDs
+
+All student prompts are defined in `src/lib/prompts/student-prompts.ts`:
+
+| ID | Name | Age | Description |
+|----|------|-----|-------------|
+| `grade_1` | 小一學生 | 7歲 | 具體思考，句子簡單，尋求認可 |
+| `grade_2` | 小二學生 | 8歲 | 開始獨立，簡單比較，同儕意識 |
+| `grade_3` | 小三學生 | 9歲 | 複雜情緒，閱讀學習，組織思考 |
+| `grade_4` | 小四學生 | 10歲 | 社會比較，同儕動態，詞彙豐富 |
+| `grade_5` | 小五學生 | 11歲 | 具體邏輯強，情緒調節，規劃能力 |
+| `grade_6` | 小六學生 | 12歲 | 抽象思考初現，身份探索，前青春期 |
+| `grade_7` | 國一學生 | 13歲 | 情緒強烈，同儕壓力，挑戰權威 |
+| `grade_8` | 國二學生 | 14歲 | 假設思考，測試邊界，社交複雜 |
+| `grade_9` | 國三學生 | 15歲 | 科學推理，未來規劃，會考壓力 |
+| `coach_direct` | 直接諮詢教練 | N/A | 直接與教練對話，無學生模擬 |
+
+**Note**: `coach_direct` is a special prompt ID for direct coach consultation without student role-play.
+
+## Available Coach Prompt IDs
+
+Coach prompts are defined in `src/lib/prompts/coach-prompts.ts`:
+
+| ID | Name | Description |
+|----|------|-------------|
+| `empathetic` | 王老師 - 同理心取向 | 著重理解、認可和情感連結。擅長建立信任關係，先同理後建議 |
+| `balanced` | 陳老師 - 平衡取向 | 結合同理心和實際建議。平衡情感支持與具體策略（**默認選項**） |
+| `structured` | 李老師 - 結構取向 | 強調行為管理和清晰界線。提供系統化方法和明確步驟 |
+
+**Default**: If not specified, `balanced` is used as the default coach prompt.
+
+## Usage Examples
+
+### Create Conversation with Grade 1 Student
+
+```bash
+curl -X POST http://localhost:3000/api/conversations/create \
+  -u "teacher_wang:cz-2025" \
+  -H "Content-Type: application/json" \
+  -d '{
+    "studentPromptId": "grade_1",
+    "coachPromptId": "empathetic"
+  }'
+```
+
+### Create Direct Coach Consultation
+
+```bash
+curl -X POST http://localhost:3000/api/conversations/create \
+  -u "teacher_wang:cz-2025" \
+  -H "Content-Type: application/json" \
+  -d '{
+    "studentPromptId": "coach_direct",
+    "coachPromptId": "balanced"
+  }'
+```
+
+### Create Conversation with Default Coach
+
+```bash
+curl -X POST http://localhost:3000/api/conversations/create \
+  -u "teacher_wang:cz-2025" \
+  -H "Content-Type: application/json" \
+  -d '{
+    "studentPromptId": "grade_7"
+  }'
+```
+
+**Note**: When `coachPromptId` is omitted, it defaults to `"balanced"`.
+
+## Use Cases
+
+1. **List all student options** - Use GET `/api/personalities` to populate a UI dropdown
+2. **Age-appropriate simulation** - Select grade level matching the student you want to practice with
+3. **Direct coach consultation** - Use `coach_direct` when you want advice without student role-play
+4. **Coaching style preference** - Choose coach persona that matches your learning style
+
+## Notes
+
+- Student prompt IDs are based on Taiwan's educational system (小一 to 國三)
+- Each grade level has developmentally appropriate language and behavior patterns
+- Coach prompts affect the tone and approach of feedback, not the accuracy
+- The `coach_direct` student prompt skips student simulation entirely
+- Prompt templates are stored with conversations, so they persist even if templates are updated
+
+## Related Operations
+
+- [Create conversation](05-create-conversation.md)
+- [Send message to student](03-send-message-to-student.md)
+- [Send message to coach](04-send-message-to-coach.md)
+
+## Reference
+
+See source code for details:
+- Student prompts: `src/lib/prompts/student-prompts.ts`
+- Coach prompts: `src/lib/prompts/coach-prompts.ts`
+- Personalities API: `src/app/api/personalities/route.ts`