feat: add GET /shows/by-episode/{episode_number} endpoint

Allows looking up shows by episode number instead of internal DB ID,
enabling IRC bot commands like !playlist 530 to resolve directly.

Made-with: Cursor

docs/api.md

@@ -117,9 +117,39 @@ Lists all shows, ordered by week start date (newest first).
 
 ---
 
+### `GET /shows/by-episode/{episode_number}`
+
+Look up a show by its episode number. This is the recommended endpoint for IRC bot integrations (e.g. `!playlist 530`).
+
+**Path Parameters**
+
+| Parameter | Type | Description |
+|-----------|------|-------------|
+| `episode_number` | integer | The episode number (e.g. 530) |
+
+**Response**
+
+```json
+{
+  "show_id": 10,
+  "episode_number": 530,
+  "week_start": "2026-03-05T02:00:00+00:00",
+  "week_end": "2026-03-12T02:00:00+00:00",
+  "tracks": [...]
+}
+```
+
+**Errors**
+
+| Status | Detail |
+|--------|--------|
+| 404 | `"No show with episode number {n}"` |
+
+---
+
 ### `GET /shows/{show_id}`
 
-Returns a specific show with its full track listing.
+Returns a specific show by internal database ID.
 
 **Path Parameters**