docs: auto-generate API route documentation

Signed-off-by: NotAShelf <raf@notashelf.dev>
Change-Id: Id0d1f9769b7ccdbf83d5fa78adef62e46a6a6964

docs/api/backup.md

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+# Backup
+
+Database backup
+
+## Endpoints
+
+### POST /api/v1/admin/backup
+
+Create a database backup and return it as a downloadable file.
+POST /api/v1/admin/backup
+
+For `SQLite`: creates a backup via VACUUM INTO and returns the file.
+For `PostgreSQL`: returns unsupported error (use `pg_dump` instead).
+
+**Authentication:** Required (Bearer JWT)
+
+#### Responses
+
+| Status | Description |
+|--------|-------------|
+| 200 | Backup file download |
+| 401 | Unauthorized |
+| 403 | Forbidden |
+| 500 | Internal server error |
+
+---
+