Add compact authenticated overview API for bot and lightweight clients

[tiankaima]

Problem

The bot's overview command has to assemble a user-facing daily summary by making several independent calls: schedules, todos, subscribed homeworks, current subscription/exams, then filtering and sorting locally.

This duplicates logic already present in server-side dashboard/MCP helpers and causes unnecessary round trips for a common lightweight client use case.

Proposed server-side feature

Add a compact authenticated overview endpoint, for example:

GET /api/me/overview?atTime=...&homeworkWindowDays=7&limit=3

Response should include the current user's:

• today schedules,
• pending todos,
• due-soon homeworks,
• upcoming exams,
• counts plus top N formatted/raw items suitable for lightweight clients.

This should be smaller than the full dashboard payload and stable enough for bots/CLI/mobile clients.

References

Server already has similar logic in MCP get_my_overview / dashboard helpers under src/lib/mcp/tools/my-data-tools.ts and src/features/home/server/*dashboard*.

Bot currently assembles this in internal/commands/commands.go overview, formatOverview, and dueSoonHomeworks.

Acceptance criteria

• One authenticated REST call returns the bot's current overview data.
• Supports anchoring to a specific time/day for testing and natural-language requests.
• Uses server-side subscription/homework/todo/exam read models instead of client fan-out.
• OpenAPI/schema docs are updated.